idx int64 0 5.62k | prompt stringlengths 885 11.1k | answers sequencelengths 8 8 | gt stringlengths 1 119 | true_reward bool 2
classes |
|---|---|---|---|---|
2,773 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given that $... | [
"The sum of the digits in the resulting product of \\(\\underbrace{9999\\cdots 99}_{80\\text{ nines}}\\) and \\(\\underbrace{7777\\cdots 77}_{80\\text{ sevens}}\\) is \\(\\boxed{640}\\).\n\nSince the code execution has already confirmed the correctness, we can conclude with:\n\n\\[\n\\boxed{640}\n\\]\n\nThe self-ev... | 720 | false |
5,259 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given the hy... | [
"Given the hyperbola $mx^2 - ny^2 = 1$ with an eccentricity of 2, we found that $\\frac{m}{n} = 3$. To verify this, let's go through the reasoning steps again:\n\n1. The given hyperbola can be rewritten in the standard form $\\frac{x^2}{\\frac{1}{m}} - \\frac{y^2}{\\frac{1}{n}} = 1$.\n2. The eccentricity $e$ is giv... | 3 | true |
1,931 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
What is the ... | [
"self-evaluate\n - The problem was solved correctly.\n - The solution was verified by solving the absolute value equation and summing the solutions.\nself-evaluate\n - The final answer is $\\boxed{\\frac{8}{3}}$.\nself-evaluate\n - You can see that the reasoning was correct and the final answer is verified.... | \frac{8}{3} | true |
1,938 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Evaluate $\s... | [
"Let's think step by step and output the final answer within \\boxed{}.",
"Let's self-evaluate:\n\n1. The problem involves evaluating square roots of squared expressions.\n2. We need to consider the absolute value of the expressions inside the square roots.\n3. Since $5 - 4\\sqrt{2}$ and $5 + 4\\sqrt{2}$ are both... | 10 | true |
899 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given vector... | [
"Your final self-evaluation should be in one of the following formats:\n - [VERIFY] correct.\n - [VERIFY] wrong.\n\nIn this case, the LCM of 441 and 5880 is 17640, which is correct.",
"You have provided the correct LCM, and your evaluation is: [VERIFY] correct.",
"Great job! You've correctly performed the s... | \frac{23}{3} | false |
4,122 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Determine th... | [
"Let's think step by step and output the final answer within \\boxed{}.",
"Given the problem of finding the greatest common divisor (GCD) of 187 and 119 and representing the result in base 5:\n\n1. We calculated the GCD of 187 and 119 using the Euclidean algorithm and found that the GCD is 17.\n2. Then we convert... | 32 | true |
1,983 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Calculate th... | [
"Let's go through the process of verifying the correctness step by step.\n\n1. **Set up the integral:**\n The volume is given by the integral:\n \\[\n V = \\int_{0}^{2\\pi} \\int_{0}^{\\sqrt{2}} \\int_{2r^2\\cos^2(\\theta) + 8r^2\\sin^2(\\theta)}^{4} r \\, dz \\, dr \\, d\\theta.\n \\]\n The innermost int... | 2\pi | true |
1,723 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given the li... | [
"Given the line \\(y = x + 1\\) intersects with the ellipse \\(mx^2 + ny^2 = 1\\) at points \\(A\\) and \\(B\\). The x-coordinate of the midpoint of the chord \\(AB\\) is \\(-\\frac{1}{3}\\). We need to find the tangent value of the angle between the two asymptotes of the hyperbola \\(\\frac{x^2}{m^2} - \\frac{y^2}... | \frac{4}{3} | true |
2,757 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
The graph of... | [
"The final answer is \\( \\boxed{3} \\).\n\nThe reasoning is as follows:\n1. The function \\( f(x) \\) is even, so \\( f(x) = f(-x) \\).\n2. The function \\( f(x) \\) is symmetric about the line \\( x = 2 \\), so \\( f(x) = f(4 - x) \\).\n3. Given \\( f(3) = 3 \\), we use the symmetry about \\( x = 2 \\) to find \\... | 3 | false |
945 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
In the posit... | [
"In the positive geometric sequence $\\{a_n\\}$, it is given that $\\lg a_3 + \\lg a_6 + \\lg a_9 = 6$. We need to determine the value of $a_5 \\cdot a_7$. \n\nFrom the previous steps, we derived that $a_1 \\cdot r^5 = 100$. This implies that $a_5 \\cdot a_7 = (a_1 \\cdot r^4) \\cdot (a_1 \\cdot r^6) = a_1^2 \\cdot... | 10000 | true |
2,610 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given that $... | [
"Let's break down the problem step-by-step and verify the solution using Python.\n\n1. **Calculate the value of \\( n \\):**\n \\[\n n = \\int_{1}^{16} \\frac{1}{\\sqrt{x}} \\, dx\n \\]\n The integral evaluates to:\n \\[\n n = \\left[ 2\\sqrt{x} \\right]_{1}^{16} = 2(4) - 2(1) = 8 - 2 = 6\n \\]\n So... | 64 | false |
1,971 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given that t... | [
"Let's perform a self-evaluation to verify the correctness of the solution. The steps we followed are:\n1. Identified the normal vector of the plane from the vector from the origin to the point $(10, -2, 5)$, which is $\\vec{n} = (10, -2, 5)$.\n2. Used the normal vector to write the equation of the plane in the for... | 10x - 2y + 5z - 129 = 0 | false |
4,593 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Find the val... | [
"To verify the correctness of the solution, we can check if the quadratic inequality $x^2 - 3x - 10 \\leq 0$ holds true for the solution set $[-2, 5]$. Let's check the boundaries and a point within the interval:\n\n1. At $x = -2$: \n \\[\n (-2)^2 - 3(-2) - 10 = 4 + 6 - 10 = 0 \\leq 0 \\quad \\text{(True)}\n \... | bc=30 | true |
2,522 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
How many pos... | [
"### Final Self-Evaluation\nYou have correctly determined that there is only one positive integer less than 1000 that is both a square and a cube, which is 1.",
"To verify the correctness of our solution, we need to ensure that:\n1. The number $n = 1$ is indeed both a square and a cube.\n2. There are no other num... | 3 | false |
4,800 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
In another c... | [
"In a mathematical reasoning competition, Kimberly's score \\( s \\) is given by the formula \\( s = 25 + 5c - w \\), where \\( c \\) is the number of correct answers and \\( w \\) is the number of wrong answers. The total number of questions is 25, so the number of unanswered questions \\( u \\) is \\( 25 - c - w ... | 100 | false |
551 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Find the rem... | [
"To verify the correctness of our solution, we can perform the polynomial division manually or check if the division algorithm holds. We can do this by multiplying the quotient by the divisor and adding the remainder to see if we get the original dividend.\n\nLet's check it step-by-step:\n\n1. The quotient and rema... | 6x - 35 | false |
3,296 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
In $\triangl... | [
"I have successfully calculated the length of side $AC$ using the Law of Cosines and verified that the result is $\\sqrt{3}$. Therefore, the final answer is $\\boxed{\\sqrt{3}}$.",
"The value of $AC$ is approximately $1.732$, which is the decimal representation of $\\sqrt{3}$. Since the exact value is $\\sqrt{3}$... | \sqrt{3} | true |
1,423 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given that p... | [
"To verify the correctness of our solution, let's analyze the reasoning and the steps taken:\n\n1. We defined the points \\(P = (a, e^a)\\) and \\(Q = (b, \\ln b)\\).\n2. The distance squared between \\(P\\) and \\(Q\\) is given by:\n \\[\n D^2 = (a - b)^2 + (e^a - \\ln b)^2\n \\]\n3. We minimized this functi... | \sqrt{2} | true |
4,775 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
How many uni... | [
"The reasoning and calculations are correct. The final answer is \\(\\boxed{18}\\).",
"Given the problem, let's perform a self-evaluation. We have calculated that the total number of unique permutations of the digits \\(3, 7, 3, 2, 2\\) is 30, and the number of permutations that start with 0 is 12. Therefore, the... | 24 | false |
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