generator large_stringclasses 1
value | id large_stringlengths 36 36 | conversations listlengths 2 2 | source large_stringclasses 1
value | thinking int64 0 0 |
|---|---|---|---|---|
Qwen3-8B | ea3dc5e5-d699-48c1-9eab-48c45d72b0f8 | [
{
"content": "Suppose ABCD is a quadrilateral with perpendicular diagonals inscribed in a circle of radius 2. What is the value of \\(AB^2 + BC^2 + CD^2 + AD^2\\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given a **cyclic quadr... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 481b8bf4-3e6a-4976-b2e8-f35f0c0b0e4a | [
{
"content": "Zoey read 15 books, one at a time. The first book took her 1 day to read, the second book took her 2 days to read, the third book took her 3 days to read, and so on, with each book taking her 1 more day to read than the previous book. Zoey finished the first book on a Monday, and the second on a W... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | a553fa2a-0556-4490-b901-95080eec6533 | [
{
"content": "Solve the following equations and inequalities: $|x-3|>-1$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the inequality:\n\n$$\n|x - 3| > -1\n$$\n\n---\n\n### Step 1: Understand the nature of absolute value\n\nT... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 2f798376-a350-41c6-ae5f-4b67d6f6ec37 | [
{
"content": "In a clothing store, a sweater that was originally priced at $73 was marked down and sold for $54.75. What was the percent amount of the markdown?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "To find the **percent amount of ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | ce6df3b4-d3a8-4a43-b629-11716afab9bb | [
{
"content": "In a right triangle, if the length of AD is 8 and the length of BD is 4, find the length of AC. Given that (BD)(DC) = 8^2 and AC^2 = (CD)(CB).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given a **right triangle** wi... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 6733648d-12d9-4946-a0bc-b5fe9aa9b5ca | [
{
"content": "Evaluate $\\cos \\pi/7 - \\cos 2\\pi/7 + \\cos 3\\pi/7.$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the expression:\n\n$$\n\\cos \\frac{\\pi}{7} - \\cos \\frac{2\\pi}{7} + \\cos \\frac{3\\pi}{7}\n$... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | da0cf3c2-5193-4cf1-860e-b51897df0f84 | [
{
"content": "Evaluate the integral $\\displaystyle \\int^{\\infty}_{0}\\sin(x^2)dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the integral:\n\n$$\n\\int_0^{\\infty} \\sin(x^2) \\, dx\n$$\n\nThis is a classic ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 302120b8-9e50-4ddf-8cbd-40bdc2ce08eb | [
{
"content": "$2\\cos^2 x+\\sin x=2$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the trigonometric equation:\n\n$$\n2\\cos^2 x + \\sin x = 2\n$$\n\n---\n\n### **Step 1: Use the Pythagorean identity**\n\nRecall the identity:... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 22fd9c63-d7a7-44b5-ba90-689f1ee30841 | [
{
"content": "David is playing a game with a fair coin. He flips the coin until the number of heads flipped minus the number of tails flipped equals 5. On average, how many flips will it take him to reach this goal?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 6bd979ea-6e5c-48eb-8400-e329d3c633b0 | [
{
"content": "Find the number of 6-digit binary strings such that each string is different from another in at least 3 digits.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find the number of **6-digit binary strings** such ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 5f5c2a85-5fa3-4344-85de-fe79972ab1d0 | [
{
"content": "Use the Fundamental Theorem of Calculus to find $\\int_S K ~ds$ where $S$ represents the half-ellipsoid $\\frac{x^2}{a^2}+\\frac{y^2}{b^2}+\\frac{z^2}{c^2}=1$ with $z \\geq 0$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 391e73b1-487b-4302-9337-25223eb70e51 | [
{
"content": "Given the numbers $e^{\\pi}$, $2^3$, $\\pi^e$, $3^2$, $3^e$, put them in increasing order.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the following numbers:\n\n- $ e^{\\pi} $\n- $ 2^3 $\n- $ \\pi^e $\n- $ 3^2 ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | c7808201-92d4-4dde-96e3-b05b7da47753 | [
{
"content": "The numbers $7$ and $5$ are written on a board. Every minute, Mr. Sterr looks at the two numbers on the board, call them $a$ and $b$, erases them, and writes $a + b$ and $|a - b|$ on the board. After $2021$ minutes, what is the ratio of the larger number to the smaller number?\nPlease reason step ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 6d617988-6c5a-427d-980f-3d1aa70d8d3b | [
{
"content": "Given a triangle \\(ABC\\), locate its orthocenter using only a compass and an unmarked ruler. No other tools are allowed (besides a pencil).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "To **locate the orthocenter** of a tr... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 3750940a-369a-46a6-aeba-79453b54dc8a | [
{
"content": "What is the smallest square frame that can cover a painting of dimensions 40 inches by 100 inches completely?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given a painting of dimensions **40 inches by 100 inches**, an... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | d37e2532-76e7-4be8-808f-5b014590df55 | [
{
"content": "A square of side length 1 and a circle of radius $\\dfrac{\\sqrt{3}}{3}$ share the same center. What is the area inside the circle but outside the square?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given:\n\n- A **s... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | c01b46ad-87b3-4d50-90ea-d22c73305942 | [
{
"content": "In how many distinct ways can 1 red, 1 blue, 1 yellow, 1 black, 1 green, and two purple beads be arranged on a circular bracelet?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find the number of **distinct way... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 88f14b99-c0ea-4fc7-a3aa-910ba27f3fe9 | [
{
"content": "In crew, an \"eight\" is a boat with four rowers on the port side and four on the starboard side. If two of the eight rowers can only row port and three can only row starboard, in how many ways can the eight rowers be assigned to the shell?\nPlease reason step by step, and put your final answer wi... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | cd28b7df-caa5-43fc-a647-24da7a8b6155 | [
{
"content": "Evaluate the expression \\(\\frac{\\cos 37^\\circ + \\sin 37^\\circ}{\\cos 37^\\circ - \\sin 37^\\circ}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the expression:\n\n$$\n\\frac{\\cos 37^\\circ ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 6907c1e4-ddf2-4165-84e7-f1707e4f63af | [
{
"content": "Find the number of 5-digit numbers that can be formed using the digits 1, 2, 4, 7, 9, and 0.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find the number of **5-digit numbers** that can be formed using the di... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | d9826336-b0e4-4789-979b-b382dee3fff4 | [
{
"content": "In a communication system, the transmitted symbols are only 1 and 0. The probability of transmitting 1 is 0.4. When transmitting 1, the probability of receiving 0 due to noise is 0.1, while when transmitting 0, the probability of receiving 1 is 0.2. What is the probability that a \"1\" is received... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | e327effc-c36b-40a5-bf9e-72cef4a83300 | [
{
"content": "What is the maximum length of a boat that can turn from a river of width \\( a \\) into a channel of width \\( b \\) that is perpendicular to the river?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given a scenario wh... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | dd9f82e0-8599-4153-8db3-1a7ed1692237 | [
{
"content": "Given two sinusoids with frequencies of $8 \\text{ kHz}$ and $3.5 \\text{ kHz}$, is the function obtained by summing these two sinusoids periodic? If so, what is the period of the resulting function?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | ddd6705f-4c2e-46d3-afd7-ddeaab88d3b9 | [
{
"content": "Given that \\( f(xy) = f(x) + f(y) + 1 \\) for \\( x, y > 0 \\) and \\( f(2) = 0 \\), find \\( f(2018) \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the functional equation:\n\n$$\nf(xy) = f(x) + f(y) + 1 \\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | ca3f967f-50f0-45e9-9e6f-11299c0fb1e8 | [
{
"content": "In a casino game, a set of numbers $S$ is given, with some numbers possibly appearing twice. You must choose a number (which does not have to be in $S$). A number is then chosen randomly from $S$, and you must pay the absolute difference between your chosen number and the randomly selected number.... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 59e41a2c-0211-4139-a8b4-7016c9cf8749 | [
{
"content": "Find the derivative of the function \\( G(t) = \\frac{mA}{A + (m - A)e^{-kmt}} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the function:\n\n$$\nG(t) = \\frac{mA}{A + (m - A)e^{-kmt}}\n$$\n\nWe are to find ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 1e517681-ea8e-46e8-badf-a63b1c55198d | [
{
"content": "In a scenario where 50 out of 270 people play Pokemon Go, and every 3 hours someone passes an RA who makes Pokemon Go players do 10 push-ups, find the expected number of days until 100 push-ups have been done. Express this expected number of days as $\\frac{m}{n}$, where $m$ and $n$ are relatively... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | dba214ec-2a77-4da9-a90f-0ca9d71163a9 | [
{
"content": "Find the sum of the number \\( N = 1234 \\) and all other four-digit numbers obtained by permutating the digits of \\( N \\) in all possible ways.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the number $ N = 12... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 7fda84d6-b8f9-4647-8d2a-e9ee84d89450 | [
{
"content": "A lane runs perpendicular to a road that is 64 feet wide. If it is just possible to carry a 125-foot long pole horizontally from the road into the lane, find the maximum width of the lane.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"c... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 07fa9b83-0c2b-4b61-bb7c-3404d9d3982c | [
{
"content": "Suppose you have $k$ teams in a tournament, each with a different skill level. In a match, the team with the higher skill level always wins. How many matches are required at a minimum to order the teams by their skill levels?\nPlease reason step by step, and put your final answer within \\boxed{}.... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 750d1400-b04c-4360-9231-cfc858f31113 | [
{
"content": "Anthony Garcia rented a car for 37 dollars a day for 7 days. There is also a charge of 45 cents for every mile driven over an average of 100 miles per day of rental, and a collision waiver of 9 dollars per day. Anthony drove 825 miles in 7 days. Gasoline costs were 49 dollars; parking and tolls we... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 0d8e73bc-f6a8-4755-8156-b9f6d2f23c14 | [
{
"content": "Solve for \\( x \\) in the equation \\( a = bx' + cx^4 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equation:\n\n$$\na = bx' + cx^4\n$$\n\nWe are asked to **solve for $ x $** in terms of the other varia... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | e6e46376-f6bb-4e34-99b4-76d22a9c80cc | [
{
"content": "An ant leaves the anthill and walks 4 feet east, then makes a $160^\\circ$ turn to the right and walks 4 more feet. If the ant continues this pattern until it reaches the anthill again, what is the total distance in feet that the ant would have walked?\nPlease reason step by step, and put your fin... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 789d9154-74c6-4ec4-b947-e2127c730baf | [
{
"content": "Write in algebraic form the product of two odd numbers and one even number, using only one variable.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to **write in algebraic form** the **product of two odd numbers a... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 15b2233f-82c1-4340-800f-8eea67129407 | [
{
"content": "Given a triangle \\(ABC\\) with the radii of the circumscribed and inscribed circles being \\(R\\) and \\(r\\) respectively, and the area of the triangle \\(ABC\\) being \\(S\\). The inscribed circle is tangent to sides \\(BC\\), \\(CA\\), and \\(AB\\) at points \\(A_1\\), \\(B_1\\), and \\(C_1\\)... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 28cf2b58-2454-4c45-9325-9d24fb1f0a65 | [
{
"content": "Solve for \\( x \\) given the equation:\n\\[\n\\tan(x) + \\tan\\left(x + \\frac{\\pi}{3}\\right) + \\tan\\left(x + \\frac{2\\pi}{3}\\right) = 3\\sqrt{3}\n\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equa... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 4f25bf6b-9ae6-4a69-8fae-18d76ee6117e | [
{
"content": "How many digits are in $a^b$ if $b = \\sqrt{9530}$ and $\\log a \\approx 2.8356$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given:\n\n- $ b = \\sqrt{9530} $\n- $ \\log a \\approx 2.8356 $\n\nWe are asked to find **... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 85a6896e-c40b-4c6b-b763-7a0335fba08f | [
{
"content": "Find a closed-form solution for \\( x \\) in the equation\n\n\\[ p = \\sum_{k=0}^{n} \\binom{n}{k} k x^k (1-x)^{n-k} \\]\n\nwhere \\( p \\in [0, n] \\). Approximations are also acceptable.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"c... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | ed802287-3e0a-4982-b737-6bed77b6370a | [
{
"content": "Let $(a_i)_{i \\in \\mathbb{N}}$ be an infinite sequence of all positive roots (in ascending order) of the equation $\\tan(x) = x$, where $x \\in \\mathbb{R}$. Find the value of $\\sum_{i=1}^\\infty \\frac{1}{a_i^2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 96cef4b2-a228-4f52-91de-1275bcfb7f0b | [
{
"content": "Calculate $\\underset{n\\to \\infty }{\\mathop{\\lim }}\\,n{{I}_{n}}\\,.$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to compute:\n\n$$\n\\lim_{n \\to \\infty} n I_n\n$$\n\nwhere $ I_n $ is some sequence. Howev... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 6fe79d9a-ca20-4609-adea-516a9b3c00e6 | [
{
"content": "Given the problem from the AMC 12A 2009, how would you solve the problem without using the triangle inequality method? The problem is as follows: A triangle has side lengths $10$, $10$, and $x$. Determine the range of values for $x$ such that the triangle is valid.\nPlease reason step by step, and... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 6f7fe0b4-05c2-43b4-a4b4-61643bfa9a8c | [
{
"content": "Find the domains of the following functions: $y=\\arccos 2^{|x|}$. &\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find the **domain** of the function:\n\n$$\ny = \\arccos(2^{|x|})\n$$\n\n---\n\n### Step 1: Un... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | def3d832-7be2-4ee6-a295-a4756d4b8c4d | [
{
"content": "Given $F \\in Isom(\\mathbb{R}^3)$ and a parallel translation $T_v \\in Isom(\\mathbb{R}^3)$ on a vector $v$, find the motion $F \\circ T_v \\circ F^{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given:\n\n- $ F ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | a04410e8-d468-4f1c-a05e-1ef1e050ddbe | [
{
"content": "An ant is at one corner of a unit cube. If the ant must travel on the box’s surface, what is the shortest distance the ant must crawl to reach the opposite corner of the cube? The distance can be written in the form $\\sqrt{a}$, where $a$ is a positive integer. Compute $a$.\nPlease reason step by ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 04c67b99-3a1f-4d33-8ebf-44f3f1341759 | [
{
"content": "Find the sum of all values of \\( k \\) that satisfy the equation \\( 2^{2k} - 2^{k+4} + 48 = 0 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equation:\n\n$$\n2^{2k} - 2^{k+4} + 48 = 0\n$$\n\n---\n\n### ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 990dc2d2-ec05-4d2a-a7d4-118b6c0ebcbf | [
{
"content": "Solve the system of equations\n\\[\n\\begin{cases}\n2^x + 3^y = 4 \\\\\n5^x + 6^y = 7\n\\end{cases}\n\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the system of equations:\n\n$$\n\\begin{cases}\n2^x + 3^y = 4... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | a4182321-806e-4a08-a4ca-aad9d4520b2d | [
{
"content": "Solve the system:\n\\[ x^3 + x(y - z)^2 = 2 \\]\n\\[ y^3 + y(z - x)^2 = 30 \\]\n\\[ z^3 + z(x - y)^2 = 16 \\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the system of equations:\n\n$$\n\\begin{cases}\nx^3 + x(... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 3d4b9a71-53fb-4d0d-9f8c-5ba09f998cdb | [
{
"content": "Let \\((a, b, c, d) \\in \\mathbb{R}^4\\) such that \\(a + b + c + d = 3\\) and \\(a^2 + b^2 + c^2 + d^2 = 45\\). Find the value of \n\\[\n\\frac{a^5}{(a-b)(a-c)(a-d)} + \\frac{b^5}{(b-a)(b-c)(b-d)} + \\frac{c^5}{(c-a)(c-b)(c-d)} + \\frac{d^5}{(d-a)(d-b)(d-c)}.\n\\]\nPlease reason step by step, an... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 08ee5a39-9e52-4aee-b75b-996e7efbca77 | [
{
"content": "Two players take turns playing on a $3 \\times 1001$ board whose squares are initially all white. Each player, in his turn, paints two squares located in the same row or column black, not necessarily adjacent. The player who cannot make his move loses the game. Determine which of the two players h... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 504aac63-491e-4dc6-8ad3-f3f7acf7163e | [
{
"content": "Given that \\( \\frac{A+B}{C-A} + \\frac{B+C}{C-B} + \\frac{A+C}{B-C} = 3 \\), calculate \\( \\frac{C+B}{C-A} + \\frac{2C}{C-B} + \\frac{A+B}{B-C} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equation:\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 7a451e89-b248-4c34-8f32-331eb31a5c23 | [
{
"content": "Solve the differential equation \\( y'' + y' + \\frac{5}{4}y = 0 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the second-order linear homogeneous differential equation:\n\n$$\ny'' + y' + \\frac{5}{4}y = 0\n... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 67d12192-6951-4a17-8926-8380caf33e3c | [
{
"content": "Evaluate the sum \\( \\sum_{k=1}^{n} \\frac{k}{2^{k-1}} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the sum:\n\n$$\n\\sum_{k=1}^{n} \\frac{k}{2^{k-1}}\n$$\n\n---\n\n### Step 1: Understand the s... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | d43b01de-d3cc-43e6-8f93-d53b22a06b05 | [
{
"content": "Let \\( f(x) \\) be a continuous function on \\([a, b]\\) where \\( a < c < b \\). If \\( f(x) > 0 \\) when \\( c < x < b \\) and \\( f(x) < 0 \\) when \\( a < x < c \\), then what is the value of the integral \\(\\int_a^b |f(x)| \\, dx\\)?\nPlease reason step by step, and put your final answer wi... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | c730929c-e058-4ffe-9bd1-6b418cbe2dd0 | [
{
"content": "For $\\text{coth}^{-1} x$, find the derivative with respect to $x$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find the derivative of the inverse hyperbolic cotangent function, $\\text{coth}^{-1} x$, with r... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 5563228b-2327-4436-8767-226a0f315d5c | [
{
"content": "Determine the measure of the solid angle at a vertex of a regular tetrahedron.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "To determine the **solid angle** at a vertex of a **regular tetrahedron**, we can use the geometric ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | f00858f1-3c23-42fe-914e-6d028de7138d | [
{
"content": "The sides of a regular icosagon inscribed in a circle have length 6. To the nearest integer, what is the diameter of the circle?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given that a **regular icosagon** (a 20-sid... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | ce62b2dd-a2d6-4a59-a0dc-6c37c0e8cc2b | [
{
"content": "Find the value of the sum $\\sum_{n=-\\infty}^{\\infty}\\frac{1}{1+n^{2}}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the infinite sum:\n\n$$\n\\sum_{n=-\\infty}^{\\infty} \\frac{1}{1 + n^2}\n$$\n... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | b8d4eb79-70d0-4d5b-9588-6e4d231d4048 | [
{
"content": "The value of \\( 21! \\) is \\( 51{,}090{,}942{,}171{,}abc{,}440{,}000 \\), where \\( a \\), \\( b \\), and \\( c \\) are digits. What is the value of \\( 100a + 10b + c \\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We a... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 0caccf08-ffc0-4793-ba85-6bbcaab7f634 | [
{
"content": "In a standard deck of 52 playing cards, Richard Rusczyke shuffles the deck and turns the cards up one by one from the top until the third ace appears. If the expected number of cards Richard will turn up is \\(\\frac{m}{n}\\) in simplest form, find \\(m + n\\).\nPlease reason step by step, and put... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | b98b829b-1cd2-438d-923d-b8f6be9c4bfc | [
{
"content": "Determine the number of digits in the number \\(2^{9876543}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to determine the **number of digits** in the number:\n\n$$\n2^{9876543}\n$$\n\n---\n\n### Step 1: Use ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 1d332a06-459b-43e1-a57b-d9ed49108df9 | [
{
"content": "Evaluate the definite integral $\\int_0^{\\frac{\\sqrt{3}}{2}} \\frac{t^2}{(1 - t^2)^{3/2}} \\, dt$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the definite integral:\n\n$$\n\\int_0^{\\frac{\\sqrt{... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 1685ec56-8b4a-4c8c-a8df-360ba13681f2 | [
{
"content": "Find \\( S_1 = \\sum_{i=0}^{n} \\frac{\\binom{k+i}{k}}{k+i} \\) where \\( m \\) and \\( k \\) are natural numbers and \\( k \\geq 2 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the sum:\n\n$$\nS_1 = \\sum_{... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | fb3cc272-1dc1-47b1-b49d-c6ff330af2a3 | [
{
"content": "What is the length of the outer handrail of a spiral staircase with a radius of 3 feet that turns 270° while rising 10 feet?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given:\n\n- **Radius of the staircase**: $ r = ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 34621660-22a2-428f-bbbe-d31bb052cc71 | [
{
"content": "Find the derivative of \\(\\frac{(3x+3)^5}{x-2}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find the derivative of the function:\n\n$$\nf(x) = \\frac{(3x + 3)^5}{x - 2}\n$$\n\nThis is a **quotient of two... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 3b9c3773-119f-45d8-99d4-6e07faad5ab8 | [
{
"content": "Evaluate the integral $$\\int_0^1 \\frac{\\ln^2 x}{x^2+x+1}dx.$$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the integral:\n\n$$\n\\int_0^1 \\frac{\\ln^2 x}{x^2 + x + 1} \\, dx\n$$\n\n---\n\n### Ste... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | adc3b713-69a6-48d7-b205-d6bf2fe8c565 | [
{
"content": "The prime numbers $a$, $b$, and $c$ satisfy the equation $a + b^2 = 4c^2$. Determine the sum of all possible values of $a + b + c$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equation:\n\n$$\na + b^2 = 4c^... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | da5b8db5-2e9b-4be1-8fb6-969f2c102422 | [
{
"content": "Solve the following equations: $\\sqrt {a-x}+\\sqrt {b+x}=\\sqrt {a+b}$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equation:\n\n$$\n\\sqrt{a - x} + \\sqrt{b + x} = \\sqrt{a + b}\n$$\n\nWe are to **solve fo... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | e442a8eb-4c90-48b4-a912-17a6368ec670 | [
{
"content": "Find the derivative of the function \\( G(t) = \\frac{mA}{A + (m - A)e^{-kmt}} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the function:\n\n$$\nG(t) = \\frac{mA}{A + (m - A)e^{-kmt}}\n$$\n\nWe are to find ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 1aa5856c-922e-4e18-8257-9db306224fe1 | [
{
"content": "Find the largest integer \\(k\\) such that \\(2^k\\) is a factor of \\(3^{512} - 1\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find the **largest integer $ k $** such that $ 2^k $ divides $ 3^{512} - 1 $... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 95d51364-deb5-4bf4-805f-dc8f5a0bd1c5 | [
{
"content": "For a positive integer $n$, let $d(n)$ be the number of $1$'s in the binary representation of $n$. What is the value of $d(1) + d(2) + \\ldots + d(512)$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given a function $... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 4ac92c19-abb8-4af4-940d-8bae0c0786e7 | [
{
"content": "Evaluate the integral \\[\\int\\limits_{ - \\infty}^\\infty \\left( \\frac{\\sin x}{x} \\right)^2 e^{itx} \\, dx.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the integral:\n\n$$\n\\int_{-\\infty}... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | c1800c4d-0ece-427d-a933-6b23034f5772 | [
{
"content": "Find the surface area of an octagonal prism with regular octagonal bases, where each side length of the bases is 5 cm and the height of the prism is 22 cm.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "To find the **surface a... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 35b51713-2b5e-449e-ab65-f67969ac9b04 | [
{
"content": "In each of $n$ houses on a straight street, there are one or more boys. At what point should all the boys meet so that the sum of the distances they walk is minimized?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "To determin... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | ced13f31-d30e-4616-9a6a-a27b32a358f3 | [
{
"content": "How many right triangles with integer side lengths are such that their side lengths are in a nonconstant geometric sequence?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find how many **right triangles with i... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | da16c3aa-4b25-4906-b662-74402cf5b165 | [
{
"content": "Let \\( ABC \\) be a triangle. Let \\( D \\) be a point inside the triangle and let \\( A' \\), \\( B' \\), and \\( C' \\) be the reflections of point \\( D \\) across sides \\( BC \\), \\( AC \\), and \\( AB \\) respectively. What is the locus of points \\( D \\) such that \\( \\triangle ABC \\si... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 3c609127-9494-4d94-aa7d-40d0c52fa73b | [
{
"content": "A triangle has sides of lengths $6, 7,$ and $8.$ What is the probability that a random point selected inside the triangle is closest to the side of length $8?$ Express your answer as a common fraction in reduced form.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 21fd5212-13cc-45f6-b49f-5e2107573df1 | [
{
"content": "Find an approximation for the integral $\\int_{0}^{\\pi/4} \\sqrt{\\sec(2x)} \\, dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to **approximate** the integral:\n\n$$\n\\int_{0}^{\\pi/4} \\sqrt{\\sec(2x)} \\,... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | d1aeae05-745c-4390-a29e-b487bcf2e228 | [
{
"content": "Given a set $S$ of 5 points in the plane, no three of which are collinear, let $A(S)$ be the largest area of a triangle formed by any three points in $S$, and $a(S)$ be the smallest area of a triangle formed by any three points in $S$. What is the minimum possible value of the ratio $A(S)/a(S)$?\n... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 38a42d23-ffae-41e8-94e4-dbe7fd4b0e68 | [
{
"content": "Calculate \\(\\lim_{n \\to \\infty} \\sum_{k=1}^{n} \\frac{1}{\\binom{2k}{k}}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to compute the limit:\n\n$$\n\\lim_{n \\to \\infty} \\sum_{k=1}^{n} \\frac{1}{\\bino... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 9db0fd1f-7fb2-48b4-a4cd-dbc641aaba4c | [
{
"content": "Calculate the indefinite integral $\\int \\frac{\\sin^3 x}{1+\\cos x}dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to compute the indefinite integral:\n\n$$\n\\int \\frac{\\sin^3 x}{1+\\cos x} \\, dx\n$$\n\n... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 1fa19cb6-be7a-4cfb-88bd-116fe439479f | [
{
"content": "Solve the differential equation \\((y')^3 - y(y')^2 - x^2y' + x^2y = 0.\\)\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the differential equation:\n\n$$\n(y')^3 - y(y')^2 - x^2y' + x^2y = 0\n$$\n\n---\n\n### **S... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 8a48b169-d429-48c8-ba4e-997b45af5d25 | [
{
"content": "Find all solutions to \\(4x^2 - 3 = 0\\) in \\(\\mod 7\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to solve the congruence:\n\n$$\n4x^2 - 3 \\equiv 0 \\pmod{7}\n$$\n\n---\n\n### Step 1: Simplify the equatio... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | f42f5789-4ded-4938-b88d-5a5d725f9d7e | [
{
"content": "Find the function \\( f(x) \\) if \\( f(a+b) - f(a-b) = 4ab \\) for all \\( a, b \\in \\mathbb{R} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the functional equation:\n\n$$\nf(a + b) - f(a - b) = 4ab \\qua... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | fc5e3b4a-b57e-4902-b518-09386baa25ee | [
{
"content": "Find the volume of a doughnut (torus) with an inner diameter of 2 cm and a boundary diameter of 2 cm. Generalize the formula for the volume of a torus given its inner and boundary diameters.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 06ec7c03-74e0-4f8b-b3ba-8018c28a66a2 | [
{
"content": "Let \\( f : R \\to S \\) be a ring homomorphism. Provide an example to show that the preimage of a maximal ideal in \\( S \\) need not be a maximal ideal in \\( R \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are give... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | a9f85417-ecbe-42d8-9bda-e2b4b4bf5e6e | [
{
"content": "Two real numbers are chosen at random between 0 and 10, inclusive. What is the probability that they are within one unit of each other? (Round to the nearest hundredth)\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are giv... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 0bbfa678-721f-454f-8a58-4a305a3b5ea2 | [
{
"content": "Evaluate the limit \\[\\lim_{n\\to \\infty} \\frac{1+\\sqrt[2^2]{2!}+\\sqrt[3^2]{3!}+\\ldots+\\sqrt[n^2]{n!}}{n}.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the limit:\n\n$$\n\\lim_{n\\to \\inft... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | fed3eb16-a782-4370-b6e8-4486f656c248 | [
{
"content": "Given a triangle $ABC$ and a point $P$, let $S_1$ be the symmetric point of $P$ with respect to $A$, $S_2$ the symmetric point of $S_1$ with respect to $B$, and $S_3$ the symmetric point of $S_2$ with respect to $C$. Find the locus of $S_3$ as $P$ moves.\nPlease reason step by step, and put your f... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-8B | 239d2964-66ec-4932-9a62-3ec1dcbbf0ab | [
{
"content": "Solve the equation $4a^3 - b^3 = 3$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equation:\n\n$$\n4a^3 - b^3 = 3\n$$\n\nWe are to **solve** this equation, which means we are looking for **all real solutions... | Nemotron-Post-Training-Dataset-v2/math | 0 |
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