generator stringclasses 1
value | id stringlengths 36 36 | conversations listlengths 2 2 | source stringclasses 1
value | thinking int64 0 0 |
|---|---|---|---|---|
Qwen3-4B | 00000052-4e27-449f-9a14-126675e67402 | [
{
"content": "Evaluate the integral $\\int_{0}^{\\frac{\\pi}{2}} \\frac{1}{(1+ \\sin \\theta)^{3}}\\ d\\theta$.\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$$\n\\int_{0}^{\\frac{\\pi}{2}... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00006ff0-65f5-419f-86ec-e63662d4888d | [
{
"content": "Skyler is at $(5,5)$ on the coordinate plane. In each step, he can move one point up or one point to the right. He will not land on any point where both the $x$ and $y$ coordinates are composite numbers. In how many ways can he reach $(21,23)$?\nPlease reason step by step, and put your final answe... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 000095a1-d64d-45af-8d74-7362aa4a9c5e | [
{
"content": "Compute the integral $$\\int_{0}^{1}\\frac{1+\\ln\\left ( 1+x \\right )}{1+x^2}dx.$$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to compute the integral:\n\n$$\n\\int_{0}^{1}\\frac{1+\\ln\\left(1+x\\right)}{1+x... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00017f47-1f6c-48b6-aea3-d250ca7bd5e4 | [
{
"content": "Let \\( f(x) = \\sum_{k=2}^{10} (\\lfloor kx \\rfloor - k \\lfloor x \\rfloor) \\), where \\( \\lfloor r \\rfloor \\) denotes the greatest integer less than or equal to \\( r \\). How many distinct values does \\( f(x) \\) assume for \\( x \\ge 0 \\)?\nPlease reason step by step, and put your fina... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0001a18c-1601-48fb-a6e5-f21868e11834 | [
{
"content": "A list of integers has mode $32$ and mean $22$. The smallest number in the list is $10$. The median $m$ of the list is a member of the list. If the list member $m$ were replaced by $m + 10$, the mean and median of the new list would be $24$ and $m + 10$, respectively. If $m$ were instead replaced ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0001f0e7-9653-436d-980c-4dd09ced86c5 | [
{
"content": "Given the matrix \\[\n A=\n \\left[ {\\begin{array}{cc}\n 1 & 4 \\\\\n -2 & 7 \\\\\n \\end{array} } \\right]\n\\], compute \\(A^{2016}\\) without using diagonalization.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0001f930-ddd2-400d-a712-702b3231091a | [
{
"content": "Evaluate \\( e^{2.9} \\) to four decimal places using a calculator.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "To evaluate $ e^{2.9} $ to four decimal places using a calculator, follow these steps:\n\n---\n\n### Step 1: Un... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 000251ef-9d8b-431f-a493-184033468c84 | [
{
"content": "Solve the equation $-5x^2 \\cos 8x = \\tan x$ for $x$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equation:\n\n$$\n-5x^2 \\cos 8x = \\tan x\n$$\n\nWe are to **solve** this equation for $ x $.\n\n---\n\n###... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 000257c7-7b1a-4327-8f5c-6fb8b740279c | [
{
"content": "Evaluate the integral $\\int \\frac{\\sin x \\cos x}{e^{3x}} \\, dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to evaluate the integral:\n\n$$\n\\int \\frac{\\sin x \\cos x}{e^{3x}} \\, dx\n$$\n\n---\n\n### ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 000279ac-e900-4b07-9acf-3ea44bbae73c | [
{
"content": "Find all triples of functions \\( p, q, r : \\mathbb{R} \\to \\mathbb{R} \\) such that for all real \\( x \\) and \\( y \\),\n\\[ p(x^3 + y) + q(x + y^3) = r(xy). \\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0002a2c3-e084-4568-aac6-f7e2877a85ca | [
{
"content": "Solve the differential equation $ty'' + (1-2t)y' - 2y = 0$ with initial conditions $y(0) = 1$ and $y'(0) = 2$ using Laplace transformation.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the second-order linear di... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00031474-119b-4bee-99a1-c65edbccce89 | [
{
"content": "Solve the equation $x^{x^{3}} = 3$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the equation:\n\n$$\nx^{x^3} = 3\n$$\n\nWe are to solve for $ x $.\n\n---\n\n### Step 1: Take logarithms on both sides\n\nTo simpl... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00033724-96b7-4ce7-b6b3-cbbeeb5563a5 | [
{
"content": "Determine all functions \\( f, g: \\mathbb{R}^+ \\rightarrow \\mathbb{R}^+ \\) such that for all positive real numbers \\( x, y \\), the following conditions hold:\n\\[ f(x + g(y)) = f(x + y) + g(y) \\]\n\\[ g(x + f(y)) = g(x + y) + f(y) \\]\nPlease reason step by step, and put your final answer w... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00038c2e-4f07-4a93-9cbd-69ec38921a8f | [
{
"content": "How many positive integers \\( n \\) between 1 and 2024 (both included) are there such that \\( \\lfloor \\sqrt{n} \\rfloor \\) divides \\( n \\)? (For \\( x \\in \\mathbb{R} \\), \\( \\lfloor x \\rfloor \\) denotes the greatest integer less than or equal to \\( x \\).)\nPlease reason step by step... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0003c2b1-48f9-4126-be0a-8f6c615cc4d5 | [
{
"content": "Find the minimum value of $n$ such that $n!$ is divisible by $10^{2014}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are asked to find the **minimum value of $ n $** such that $ n! $ is divisible by $ 10^{2014} $.\n\n--... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00044615-e752-46d5-ad2e-e10b05d6a222 | [
{
"content": "Given a regular octagon $ABCDEFGH$ with a point $X$ inside such that $XM \\perp AB$, $XN \\perp CD$, and $BM = DN$. If $XM = 31$ and $XN = 29$, can we find the side length of the octagon? If yes, find it.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00045b56-9891-4c8f-b644-8dd1dd24e5c4 | [
{
"content": "Let \\( n \\) be an odd positive number greater than 1 such that \\( n \\mid 2023^n - 1 \\). Find the two smallest values of such \\( n \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given that $ n $ is an **odd po... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 000485f0-a1f4-4df7-adea-2b2b8e733490 | [
{
"content": "Find all real numbers \\( x \\) such that \\( \\frac{\\sqrt{x}}{x\\sqrt{x} - 3\\sqrt{x} + 3} \\) is an integer.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the expression:\n\n$$\n\\frac{\\sqrt{x}}{x\\sqrt{x} - ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0004bbba-df9b-471f-8e39-4a35ad568e52 | [
{
"content": "Determine the range of \\( m \\) such that the function \\( f(x) = \\begin{cases} \n\\frac{(x-m)^2}{|x-m|}, & x \\neq 1 \\\\ \n1, & x = 1 \n\\end{cases} \\) has a local maximum at \\( x = 1 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0004f7b8-7e52-4b7e-b9d8-e47021bc551f | [
{
"content": "A finite sequence \\(a_0, a_1, \\ldots, a_n\\) of integers is called a curious sequence if for every \\(k = 0, 1, 2, \\ldots, n\\), the number of times \\(k\\) appears in the sequence is \\(a_k\\). Given a curious sequence \\(a_0, a_1, \\ldots, a_{2011}\\), what is the value of the sum \\(\\sum_{k... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0005468f-e548-431d-a4e2-f86b19b33b38 | [
{
"content": "Find all whole numbers \\( x, y, z \\) such that:\n\\[ x + y + z \\equiv 0 \\pmod{2018} \\]\nand\n\\[ x^y + y^z = 2018^z - xy \\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the following system of congruences ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00054fb9-74a5-488c-ae01-022248e01c3b | [
{
"content": "If \\( x, y, \\) and \\( z \\) are positive real numbers and \\( xyz(x+y+z) = 9 \\), find the minimum value of \\( (x+y)^2 + 4(y+z)^2 + (z+x)^2 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given that $ x, y, z $ ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00056ba7-47a0-4f26-b472-811c40a9bded | [
{
"content": "Find all matrices \\( A \\in \\mathcal{M}_n(\\mathbb{C}) \\) such that for all permutation matrices \\( P \\), the spectrum \\( \\sigma(PA) = \\sigma(A) \\). Here, \\( \\sigma(\\cdot) \\) denotes the spectrum.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0005b7dc-644d-4b8b-922f-da3dd7187b66 | [
{
"content": "Let \\( S \\) be the Sierpiński triangle. What can be said about the Hausdorff dimension of the elevation sets \\( f^{-1}(y) \\) for typical continuous real functions defined on \\( S \\)? (A property is satisfied for typical continuous real functions on \\( S \\) if the set of functions not havin... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0005bf69-24e6-4b40-9712-cafa73d6dea2 | [
{
"content": "Find the equation of the line \\( l \\) that is tangent to both parabolas \\( y = x^2 + ax \\) and \\( y = x^2 - 2ax \\), where \\( a \\) is a positive constant.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given two ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0006175b-9f37-4417-b73f-6b2ded475eb3 | [
{
"content": "Solve the inequality \\( x(x+2)(x-7) \\leq 0 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the inequality:\n\n$$\nx(x+2)(x-7) \\leq 0\n$$\n\n---\n\n### **Step 1: Find the critical points**\n\nThe expression ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 000631a0-9111-4a2a-8b82-1f10a49fc611 | [
{
"content": "A library charges 100 cents for borrowing a book. For late returns, the fines are as follows: the first 10 days are penalized at 10% per day, the next 10 days at 15% per day, the next 10 days at 20% per day, and so on. Calculate the total fines for a book returned 4 months late, assuming each mont... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00065b40-855b-47a1-a7e0-2876feb80ad7 | [
{
"content": "Determine whether the subset \\( A = \\{z \\in \\mathbb{C} \\mid z \\neq 0, \\text{Arg}(z^2) \\in [0, \\frac{\\pi}{4})\\} \\) is open, closed, and/or connected. Note: The principal argument of a non-zero complex number \\( w \\), denoted by \\( \\text{Arg}(w) \\), is defined to be the unique argum... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00065e8a-59c3-43b8-80d2-b5bdbebedb49 | [
{
"content": "Mort spilled half the contents of a pitcher of orange juice and then filled the half-full pitcher with water. He poured himself a glass of the diluted orange juice, leaving the pitcher $3/4$ full. He then filled the pitcher to the top with double strength orange juice. Compare the concentration of... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 000671a6-2a28-4c60-b878-7c06be6a9cdd | [
{
"content": "You have a 4-digit whole number that is a perfect square. Another number is formed by adding 1 to the unit's digit, subtracting 1 from the ten's digit, adding 1 to the hundred's digit, and subtracting 1 from the thousand's digit. If the resulting number is also a perfect square, find the original ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00068548-550a-4c9f-bd03-c3aeacfcdd13 | [
{
"content": "Let \\(a, b, t\\) be real numbers such that \\(a \\geq 0 > b\\). Define sequences \\(a_n, b_n\\) for \\(n = 1, 2, \\cdots\\) as follows:\n\\[a_1 = a, \\quad b_1 = b\\]\n\\[a_{n+1} = \\left(\\frac{t}{2} + \\frac{5}{t^2 + 1}\\right)a_n + \\left(\\frac{t}{2} - \\frac{5}{t^2 + 1}\\right)b_n\\]\n\\[b_{... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00069a69-65b4-4fd5-beed-9538cd2f21c6 | [
{
"content": "The set $A$ consists of $m$ consecutive integers with a sum of $2m$. The set $B$ consists of $n$ consecutive integers with a sum of $2n$. The difference between the largest elements of sets $A$ and $B$ is 99. Find the value of $m$.\nPlease reason step by step, and put your final answer within \\bo... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0006aa59-b32b-43fd-ba66-0b7c322aa8e9 | [
{
"content": "Let \\( G(n,m) \\) be the 1-graphs with \\( n \\) vertices and \\( m \\) edges. Given the characteristic polynomial \\( P(\\lambda) = \\lambda^4 - 3\\lambda^2 + 1 \\), determine the spectrum \\( \\operatorname{spec}(G) \\) and study if these graphs are cospectral. Additionally, describe the planar... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0006ccf1-105e-480c-977e-fefcb1125d9f | [
{
"content": "Let \\( S \\) be the set of \\( 2 \\times 2 \\) matrices over \\( \\mathbb{F}_p \\) with trace \\( 1 \\) and determinant \\( 0 \\). Determine the size \\( |S| \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given a ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 000702d4-9aee-44cc-89e5-973f0809b992 | [
{
"content": "$\\frac{1}{2}\\sin 3x+\\frac{\\sqrt 3}{2}\\cos 3x=\\sin 5x$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given the trigonometric equation:\n\n$$\n\\frac{1}{2}\\sin 3x + \\frac{\\sqrt{3}}{2}\\cos 3x = \\sin 5x\n$$\n\n... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00070c28-bd87-4be1-aa45-ee67b5d797e4 | [
{
"content": "There are 60 matchsticks and two players, A and B. Each player can only take any perfect square amount of matchsticks (1, 4, 9, 16, 25, etc.) each turn. The person to take the last matchstick wins. Does a winning strategy exist for player A?\nPlease reason step by step, and put your final answer w... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00073b22-1f7e-4d61-a527-ec43bbf856c7 | [
{
"content": "Which base 8 positive 3-digit integer, when multiplied by 2, has its digits switched? (i.e., $[abc]_{8} \\times 2 = [cba]_{8}$).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We are given a **base 8** positive **3-digit integ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00076358-9a19-44aa-9c18-3cb83b92c1a0 | [
{
"content": "In triangle $ABC$ with side lengths $13, 14, 15$, where should point $P$ be chosen to minimize the sum of the distances $PA + PB + PC$? Is it the circumcenter or somewhere else?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "W... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 0008748b-af8d-4a25-8e34-e3771ea55713 | [
{
"content": "Let \\( x, y, z \\) be positive real numbers such that \\( x^2 + y^2 = 49 \\), \\( y^2 + yz + z^2 = 36 \\), and \\( x^2 + \\sqrt{3}xz + z^2 = 25 \\). If the value of \\( 2xy + \\sqrt{3}yz + zx \\) can be written as \\( p \\sqrt{q} \\) where \\( p, q \\in \\mathbb{Z} \\) and \\( q \\) is squarefree... | Nemotron-Post-Training-Dataset-v2/math | 0 |
Qwen3-4B | 00089193-53d6-47fa-86cc-10081692f6f7 | [
{
"content": "A tangent $\\overline{MA}$ is drawn from a point $M$ to circle $O$. $\\overline{MC}$ is a secant line intersecting $O$ at $B$. Given that $\\angle AMC$'s bisector intersects $\\overline{AC}$ at $E$ and $\\overline{AB}$ at $D$, compute $\\frac{DB}{AB} + \\frac{EC}{AC}$.\nPlease reason step by step,... | Nemotron-Post-Training-Dataset-v2/math | 0 |
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