data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "19990",
"style": "rule"
} | {
"index": 2472,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"index": 542,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "-47.5",
"style": "rule"
} | {
"index": 1432,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "In right triangle $ABC$ with $\\angle B = 90^\\circ$, we have $AB = 8$ and $AC = 6$. Find $\\cos C$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{5}",
"style": "rule"
} | {
"index": 281,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "Calculate the sum of the series $\\sum_{n=1}^{\\infty} \\frac{(-1)^{n+1}}{n^{5}}$ with an accuracy of $10^{-3}$.",
"role": "user"
}
] | math | {
"ground_truth": "0.973",
"style": "rule"
} | {
"index": 1002,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "Kelvin the Frog and 10 of his relatives are at a party. Every pair of frogs is either friendly or unfriendly. When 3 pairwise friendly frogs meet up, they will gossip about one another and end up in a fight (but stay friendly anyway). When 3 pairwise unfriendly frogs meet up, they will also end up... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"index": 1516,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"index": 1169,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"index": 646,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "637",
"style": "rule"
} | {
"index": 2316,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Let $a,$ $b,$ $c$ be nonzero real numbers such that $a + b + c = 0,$ and $ab + ac + bc \\neq 0.$ Find all possible values of\n\\[\n\\frac{a^7 + b^7 + c^7}{abc (ab + ac + bc)}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"index": 1242,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "392",
"style": "rule"
} | {
"index": 2174,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 32,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "A total area of \\( 2500 \\, \\mathrm{m}^2 \\) will be used to build identical houses. The construction cost for a house with an area \\( a \\, \\mathrm{m}^2 \\) is the sum of the material cost \\( 100 p_{1} a^{\\frac{3}{2}} \\) yuan, labor cost \\( 100 p_{2} a \\) yuan, and other costs \\( 100 p_... | math | {
"ground_truth": "156",
"style": "rule"
} | {
"index": 1229,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{1}{12}",
"style": "rule"
} | {
"index": 424,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "In quadrilateral \\(ABCD\\), \\(\\angle ABD = 70^\\circ\\), \\(\\angle CAD = 20^\\circ\\), \\(\\angle BAC = 48^\\circ\\), \\(\\angle CBD = 40^\\circ\\). Find \\(\\angle ACD\\).",
"role": "user"
}
] | math | {
"ground_truth": "22",
"style": "rule"
} | {
"index": 550,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "225",
"style": "rule"
} | {
"index": 2452,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "086231",
"style": "rule"
} | {
"index": 472,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"index": 438,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{1}{5}",
"style": "rule"
} | {
"index": 2461,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"index": 1117,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "2007",
"style": "rule"
} | {
"index": 1156,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "The value $b^n$ has both $b$ and $n$ as positive integers less than or equal to 15. What is the greatest number of positive factors $b^n$ can have?",
"role": "user"
}
] | math | {
"ground_truth": "496",
"style": "rule"
} | {
"index": 863,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "8^{1/8}",
"style": "rule"
} | {
"index": 1407,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1089",
"style": "rule"
} | {
"index": 833,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Find four distinct positive integers $a, b, c, d$ less than $15$ which are invertible modulo $15$. Calculate the remainder when $(abc + abd + acd + bcd)(abcd)^{-1}$ is divided by $15$.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 1083,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "628",
"style": "rule"
} | {
"index": 2077,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"index": 2344,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 1030,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"index": 208,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Triangle $\\triangle ABC$ in the figure has area $10$. Points $D, E$ and $F$, all distinct from $A, B$ and $C$, \nare on sides $AB, BC$ and $CA$ respectively, and $AD = 2, DB = 3$. If triangle $\\triangle ABE$ and quadrilateral $DBEF$ \nhave equal areas, then that area is",
"role": "user"
}
... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 378,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1, 2, 3, 5",
"style": "rule"
} | {
"index": 2280,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 1135,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"index": 180,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1 - \\frac{6}{\\pi^2}",
"style": "rule"
} | {
"index": 14,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Given the harmonic mean of the first n terms of the sequence $\\left\\{{a}_{n}\\right\\}$ is $\\dfrac{1}{2n+1}$, and ${b}_{n}= \\dfrac{{a}_{n}+1}{4}$, find the value of $\\dfrac{1}{{b}_{1}{b}_{2}}+ \\dfrac{1}{{b}_{2}{b}_{3}}+\\ldots+ \\dfrac{1}{{b}_{10}{b}_{11}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{10}{11}",
"style": "rule"
} | {
"index": 1369,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"index": 535,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "A farmer builds a rectangular chicken coop that leans against a wall, covering an area of 36m<sup>2</sup>. Due to geographical constraints, the length of the side of the chicken coop, $x$, cannot exceed 7m. The wall height is 2m. The cost of constructing the front of the chicken coop is 40 yuan/m<... | math | {
"ground_truth": "2760",
"style": "rule"
} | {
"index": 1074,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "Solve the equation $x^2 + 14x = 72$. The positive solution has the form $\\sqrt{c} - d$ for positive natural numbers $c$ and $d$. What is $c + d$?",
"role": "user"
}
] | math | {
"ground_truth": "128",
"style": "rule"
} | {
"index": 2350,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "When someone tries to withdraw money from an ATM with a forgotten last digit of the password, calculate the probability that they will press the correct digit in no more than 2 attempts.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{1}{5}",
"style": "rule"
} | {
"index": 1814,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"index": 1755,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"index": 39,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "2.8",
"style": "rule"
} | {
"index": 2342,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "10 + 2\\sqrt{10}",
"style": "rule"
} | {
"index": 2327,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "424",
"style": "rule"
} | {
"index": 610,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "From the set \\( M = \\{1, 2, \\cdots, 2008\\} \\) of the first 2008 positive integers, a \\( k \\)-element subset \\( A \\) is chosen such that the sum of any two numbers in \\( A \\) cannot be divisible by the difference of those two numbers. What is the maximum value of \\( k \\)?",
"role":... | math | {
"ground_truth": "670",
"style": "rule"
} | {
"index": 147,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "Squares $ABCD$ and $EFGH$ are congruent, $AB=10$, and $G$ is the center of square $ABCD$. The area of the region in the plane covered by these squares is",
"role": "user"
}
] | math | {
"ground_truth": "175",
"style": "rule"
} | {
"index": 1515,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{9}{8}",
"style": "rule"
} | {
"index": 606,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "288",
"style": "rule"
} | {
"index": 1764,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 522,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"index": 171,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"index": 1265,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 1496,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "0.5",
"style": "rule"
} | {
"index": 163,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"index": 1468,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 861,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{15}{8} - 2\\ln 2",
"style": "rule"
} | {
"index": 1024,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "503",
"style": "rule"
} | {
"index": 421,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{153}{1180}",
"style": "rule"
} | {
"index": 1451,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Coordinate System and Parametric Equation\nGiven the ellipse $(C)$: $\\frac{x^{2}}{16} + \\frac{y^{2}}{9} = 1$, which intersects with the positive semi-axis of $x$ and $y$ at points $A$ and $B$ respectively. Point $P$ is any point on the ellipse. Find the maximum area of $\\triangle PAB$.",
"r... | math | {
"ground_truth": "6(\\sqrt{2} + 1)",
"style": "rule"
} | {
"index": 2250,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "180001",
"style": "rule"
} | {
"index": 633,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "504",
"style": "rule"
} | {
"index": 971,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"index": 665,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{137}{24}-8 \\ln 2",
"style": "rule"
} | {
"index": 725,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 1691,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1013",
"style": "rule"
} | {
"index": 101,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "In an isosceles trapezoid \\(ABCD\\) (\\(BC \\parallel AD\\)), the angles \\(ABD\\) and \\(DBC\\) are \\(135^{\\circ}\\) and \\(15^{\\circ}\\) respectively, and \\(BD = \\sqrt{6}\\). Find the perimeter of the trapezoid.",
"role": "user"
}
] | math | {
"ground_truth": "9 - \\sqrt{3}",
"style": "rule"
} | {
"index": 734,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "2.7",
"style": "rule"
} | {
"index": 1363,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "The numbers \\(a, b, c, d\\) belong to the interval \\([-4.5, 4.5]\\). Find the maximum value of the expression \\(a + 2b + c + 2d - ab - bc - cd - da\\).",
"role": "user"
}
] | math | {
"ground_truth": "90",
"style": "rule"
} | {
"index": 1689,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "5.21",
"style": "rule"
} | {
"index": 1018,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1001",
"style": "rule"
} | {
"index": 2368,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 652,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"index": 442,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"index": 1569,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{162}{625}",
"style": "rule"
} | {
"index": 158,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"index": 1934,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{6}{7}",
"style": "rule"
} | {
"index": 913,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "630",
"style": "rule"
} | {
"index": 817,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "29/24",
"style": "rule"
} | {
"index": 1892,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Given the function $f(x)={(3\\ln x-x^{2}-a-2)}^{2}+{(x-a)}^{2}$ $(a\\in \\mathbb{R})$, determine the value of the real number $a$ such that the inequality $f(x)\\leqslant 8$ has solutions for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"index": 1435,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 1253,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1010",
"style": "rule"
} | {
"index": 934,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "588",
"style": "rule"
} | {
"index": 915,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"index": 96,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "7.5",
"style": "rule"
} | {
"index": 791,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "A company sells a brand of cars in two places, A and B, with profits (in units of 10,000 yuan) of $L_{1}=-x^{2}+21x$ and $L_{2}=2x$ respectively, where $x$ is the sales volume (in units). If the company sells a total of 15 cars in both places, what is the maximum profit it can achieve?",
"role... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"index": 1635,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"index": 1347,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Little Pang, Little Dingding, Little Ya, and Little Qiao's four families, totaling 8 parents and 4 children, went to the amusement park together. The ticket prices are as follows: adult tickets are 100 yuan per person; children's tickets are 50 yuan per person; if there are 10 or more people, they... | math | {
"ground_truth": "800",
"style": "rule"
} | {
"index": 1143,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{3}{2} + \\sqrt{3}",
"style": "rule"
} | {
"index": 2440,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"index": 1145,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "98",
"style": "rule"
} | {
"index": 1441,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "306",
"style": "rule"
} | {
"index": 2093,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"index": 1640,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"index": 1359,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Analogous to the exponentiation of rational numbers, we define the division operation of several identical rational numbers (all not equal to $0$) as \"division exponentiation,\" denoted as $a^{ⓝ}$, read as \"$a$ circle $n$ times.\" For example, $2\\div 2\\div 2$ is denoted as $2^{③}$, read as \"$... | math | {
"ground_truth": "-73",
"style": "rule"
} | {
"index": 113,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "How many numbers between 10 and 13000, when read from left to right, are formed by consecutive digits in ascending order? For example, 456 is one of these numbers, but 7890 is not.",
"role": "user"
}
] | math | {
"ground_truth": "22",
"style": "rule"
} | {
"index": 2173,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "\\frac{5}{18}",
"style": "rule"
} | {
"index": 1071,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "18 \\pi",
"style": "rule"
} | {
"index": 2358,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "Two cars, $A$ and $B$, depart from one city to another. In the first 5 minutes, they traveled the same distance. Then, due to an engine failure, $B$ had to reduce its speed to 2/5 of its original speed, and thus arrived at the destination 15 minutes after car $A$, which continued at a constant spe... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"index": 2202,
"no_hint_prompt": true,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "63",
"style": "rule"
} | {
"index": 156,
"no_hint_prompt": false,
"split": "train"
} | |
[
{
"content": "# GENERATOR (PROBLEM SOLVER)\n\nInstruction: You are an expert problem-solving assistant tasked with analyzing and solving various questions using a combination of your expertise and provided reference materials. Each task will include:\n1. A specific question or problem to solve\n2. A cheatsheet ... | math | {
"ground_truth": "1333\\frac{1}{3}",
"style": "rule"
} | {
"index": 444,
"no_hint_prompt": false,
"split": "train"
} |
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