data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Find the integer $n,$ $0 \\le n \\le 180,$ such that $\\cos n^\\circ = \\cos 758^\\circ.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "38"
} | {
"split": "train",
"index": 27449,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The secret object is a rectangle measuring $200 \\times 300$ meters. Outside the object, there is one guard stationed at each of its four corners. An intruder approached the perimeter of the secret object from the outside, and all the guards ran towards the intruder using the s... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 27450,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the value of $k$ such that the equation\n\\[\\frac{x + 3}{kx - 2} = x\\] has exactly one solution. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{4}"
} | {
"split": "train",
"index": 27451,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the graph of the power function $y=f(x)$ passes through the point $\\left( \\frac{1}{2}, \\frac{\\sqrt{2}}{2} \\right)$, then $\\lg [f(2)]+\\lg [f(5)]=$ \\_\\_\\_\\_\\_\\_ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 27452,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$, $b$, $c$, $a+b-c$, $a+c-b$, $b+c-a$, $a+b+c$ be seven distinct prime numbers, and among $a$, $b$, $c$, the sum of two numbers is 800. Let $d$ be the difference between the largest and the smallest of these seven prime numbers. Find the maximum possible value of $d$. Le... | math | {
"style": "rule",
"ground_truth": "1594"
} | {
"split": "train",
"index": 27453,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest prime number $p$ that cannot be represented in the form $|3^{a} - 2^{b}|$, where $a$ and $b$ are non-negative integers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "41"
} | {
"split": "train",
"index": 27454,
"solution": "\nWe need to find the smallest prime number \\( p \\) that cannot be represented in the form \\( |3^a - 2^b| \\), where \\( a \\) and \\( b \\) are non-negative integers.\n\nFirst, we verify that all primes less than 41 can be expressed in the form \\( |3^a - 2^b| ... |
deepscaler | [
{
"role": "user",
"content": "Let $P$ be a moving point on the line $3x+4y+3=0$, and through point $P$, draw two tangents to the circle $C$: $x^{2}+y^{2}-2x-2y+1=0$, with the points of tangency being $A$ and $B$, respectively. Find the minimum value of the area of quadrilateral $PACB$. Let's think step by s... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 27455,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The expression $\\frac{\\sqrt{3}\\tan 12^{\\circ} - 3}{(4\\cos^2 12^{\\circ} - 2)\\sin 12^{\\circ}}$ equals \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4\\sqrt{3}"
} | {
"split": "train",
"index": 27456,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\( ABC \\), the sides \\( AC = 14 \\) and \\( AB = 6 \\) are known. A circle with center \\( O \\), constructed on side \\( AC \\) as its diameter, intersects side \\( BC \\) at point \\( K \\). It is given that \\(\\angle BAK = \\angle ACB\\). Find the area of tri... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 27457,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify and find the value of: $a^{2}-\\left(a-\\dfrac{2a}{a+1}\\right)\\div \\dfrac{a^{2}-2a+1}{a^{2}-1}$, where $a$ is a solution of the equation $x^{2}-x-\\dfrac{7}{2}=0$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{7}{2}"
} | {
"split": "train",
"index": 27458,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number $2013$ is expressed in the form $2013 = \\frac {a_1!a_2!...a_m!}{b_1!b_2!...b_n!}$,where $a_1 \\ge a_2 \\ge \\cdots \\ge a_m$ and $b_1 \\ge b_2 \\ge \\cdots \\ge b_n$ are positive integers and $a_1 + b_1$ is as small as possible. What is $|a_1 - b_1|$? Let's think ... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 27459,
"solution": "1. **Prime Factorization of 2013**: \n The first step is to find the prime factorization of 2013. We find that:\n \\[\n 2013 = 3 \\times 11 \\times 61\n \\]\n This indicates that any expression for 2013 in terms of factorials must include these prime fact... |
deepscaler | [
{
"role": "user",
"content": "Train 109 T departs from Beijing at 19:33 and arrives in Shanghai the next day at 10:26; train 1461 departs from Beijing at 11:58 and arrives in Shanghai the next day at 8:01. How many minutes are the running times of these two trains different? Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "310"
} | {
"split": "train",
"index": 27460,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(\\omega\\) denote the incircle of triangle \\(ABC\\). The segments \\(BC, CA\\), and \\(AB\\) are tangent to \\(\\omega\\) at \\(D, E\\), and \\(F\\), respectively. Point \\(P\\) lies on \\(EF\\) such that segment \\(PD\\) is perpendicular to \\(BC\\). The line \\(AP\\) ... | math | {
"style": "rule",
"ground_truth": "196"
} | {
"split": "train",
"index": 27461,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dr. Math's four-digit house number $WXYZ$ contains no zeroes and can be split into two different two-digit primes ``$WX$'' and ``$YZ$'' where the digits $W$, $X$, $Y$, and $Z$ are not necessarily distinct. If each of the two-digit primes is less than 50, how many such house num... | math | {
"style": "rule",
"ground_truth": "110"
} | {
"split": "train",
"index": 27462,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a_n\\}$ satisfies $a_n + (-1)^{n+1}a_{n+1} = 2n - 1$, find the sum of the first 40 terms, $S_{40}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "780"
} | {
"split": "train",
"index": 27463,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The remainder can be defined for all real numbers $x$ and $y$ with $y \\neq 0$ by $\\text{rem} (x ,y)=x-y\\left \\lfloor \\frac{x}{y} \\right \\rfloor$ where $\\left \\lfloor \\tfrac{x}{y} \\right \\rfloor$ denotes the greatest integer less than or equal to $\\tfrac{x}{y}$. Wha... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{40}"
} | {
"split": "train",
"index": 27464,
"solution": "1. **Definition of Remainder**: The remainder function $\\text{rem}(x, y)$ for real numbers $x$ and $y$ (with $y \\neq 0$) is defined as:\n \\[\n \\text{rem}(x, y) = x - y \\left\\lfloor \\frac{x}{y} \\right\\rfloor\n \\]\n where $\\left\\lfloor \\cdot \\ri... |
deepscaler | [
{
"role": "user",
"content": "(1) When $x \\in \\left[\\frac{\\pi}{6}, \\frac{7\\pi}{6}\\right]$, find the maximum value of the function $y = 3 - \\sin x - 2\\cos^2 x$. \n(2) Given that $5\\sin\\beta = \\sin(2\\alpha + \\beta)$ and $\\tan(\\alpha + \\beta) = \\frac{9}{4}$, find $\\tan \\alpha$. Let's think... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 27465,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The time it takes for person A to make 90 parts is the same as the time it takes for person B to make 120 parts. It is also known that A and B together make 35 parts per hour. Determine how many parts per hour A and B each make. Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 27466,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the infinite geometric series: $$\\frac{4}{3} - \\frac{5}{12} + \\frac{25}{144} - \\frac{125}{1728} + \\dots$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{64}{63}"
} | {
"split": "train",
"index": 27467,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For each positive integer $n$, let $f_1(n)$ be twice the number of positive integer divisors of $n$, and for $j \\ge 2$, let $f_j(n) = f_1(f_{j-1}(n))$. For how many values of $n \\le 50$ is $f_{50}(n) = 12?$ Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 27468,
"solution": "We are given a function $f_1(n)$ which is twice the number of positive integer divisors of $n$, and for $j \\geq 2$, $f_j(n) = f_1(f_{j-1}(n))$. We need to find how many values of $n \\leq 50$ satisfy $f_{50}(n) = 12$.\n\n#### Step 1: Understanding $f_1(n)$\nThe fu... |
deepscaler | [
{
"role": "user",
"content": "How many diagonals does a regular seven-sided polygon contain? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 27469,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the line $l: \\sqrt{3}x-y-4=0$, calculate the slope angle of line $l$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{3}"
} | {
"split": "train",
"index": 27470,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 7 people standing in a row. How many different arrangements are there according to the following requirements?\n\n(1) Among them, A cannot stand at the head, and B cannot stand at the tail;\n(2) Among them, A, B, and C must stand next to each other;\n(3) Among them, A... | math | {
"style": "rule",
"ground_truth": "840"
} | {
"split": "train",
"index": 27471,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the ellipse \\\\(C: \\dfrac{x^2}{a^2} + \\dfrac{y^2}{b^2} = 1, (a > b > 0)\\\\) have an eccentricity of \\\\(\\dfrac{2\\sqrt{2}}{3}\\\\), and it is inscribed in the circle \\\\(x^2 + y^2 = 9\\\\).\n\n\\\\((1)\\\\) Find the equation of ellipse \\\\(C\\\\).\n\n\\\\((2)\\\\) A... | math | {
"style": "rule",
"ground_truth": "-\\dfrac{9}{4}"
} | {
"split": "train",
"index": 27472,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of ordered triples of divisors $(d_{1}, d_{2}, d_{3})$ of 360 such that $d_{1} d_{2} d_{3}$ is also a divisor of 360. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "800"
} | {
"split": "train",
"index": 27473,
"solution": "Since $360=2^{3} \\cdot 3^{2} \\cdot 5$, the only possible prime divisors of $d_{i}$ are 2,3 , and 5 , so we can write $d_{i}=2^{a_{i}} \\cdot 3^{b_{i}} \\cdot 5^{c_{i}}$, for nonnegative integers $a_{i}, b_{i}$, and $c_{i}$. Then, $d_{1} d_{2} d_{3} \\mid 360$ if ... |
deepscaler | [
{
"role": "user",
"content": "A decorative garden is designed with a rectangular lawn with semicircles of grass at either end. The ratio of the length of the rectangle to its width is 5:4, and the total length including the semicircles is 50 feet. Calculate the ratio of the area of the rectangle to the comb... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{\\pi}"
} | {
"split": "train",
"index": 27474,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point $P$ is located inside triangle $ABC$ so that angles $PAB, PBC,$ and $PCA$ are all congruent. The sides of the triangle have lengths $AB=13, BC=14,$ and $CA=15.$ Find $\\tan \\angle PAB.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{168}{295}"
} | {
"split": "train",
"index": 27475,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(a) A natural number $n$ is less than 120. What is the largest remainder that the number 209 can give when divided by $n$?\n\n(b) A natural number $n$ is less than 90. What is the largest remainder that the number 209 can give when divided by $n$? Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "69"
} | {
"split": "train",
"index": 27476,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers \\( 62, 63, 64, 65, 66, 67, 68, 69, \\) and \\( 70 \\) are divided by, in some order, the numbers \\( 1, 2, 3, 4, 5, 6, 7, 8, \\) and \\( 9 \\), resulting in nine integers. The sum of these nine integers is \\( S \\). What are the possible values of \\( S \\)? Let's... | math | {
"style": "rule",
"ground_truth": "187"
} | {
"split": "train",
"index": 27477,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the largest integer less than $\\log_2 \\frac{3}{2} + \\log_2 \\frac{6}{3} + \\cdots + \\log_2 \\frac{3030}{3029}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 27478,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A fair six-sided die is rolled 3 times. If the sum of the numbers rolled on the first two rolls is equal to the number rolled on the third roll, what is the probability that at least one of the numbers rolled is 2? Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{15}"
} | {
"split": "train",
"index": 27479,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given three natural numbers 1, 2, 3, perform an operation by replacing one of these numbers with the sum of the other two. After performing this operation 9 times, what is the maximum possible value of the largest number among the resulting three natural numbers? Let's think st... | math | {
"style": "rule",
"ground_truth": "233"
} | {
"split": "train",
"index": 27480,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a_n\\}$ where $a_n = n$, for each positive integer $k$, in between $a_k$ and $a_{k+1}$, insert $3^{k-1}$ twos (for example, between $a_1$ and $a_2$, insert three twos, between $a_2$ and $a_3$, insert $3^1$ twos, between $a_3$ and $a_4$, insert $3^2$ twos, e... | math | {
"style": "rule",
"ground_truth": "245"
} | {
"split": "train",
"index": 27481,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each of 100 students sends messages to 50 different students. What is the least number of pairs of students who send messages to each other? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 27482,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two trains, each composed of 15 identical cars, were moving towards each other at constant speeds. Exactly 28 seconds after their first cars met, a passenger named Sasha, sitting in the compartment of the third car, passed by a passenger named Valera in the opposite train. More... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 27483,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute: \\(93 \\times 107\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9951"
} | {
"split": "train",
"index": 27484,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $|\\cos\\theta|= \\frac {1}{5}$ and $\\frac {5\\pi}{2}<\\theta<3\\pi$, find the value of $\\sin \\frac {\\theta}{2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{15}}{5}"
} | {
"split": "train",
"index": 27485,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $\\triangle ABC$, with side lengths $AB=2$ and $BC=4$, and angle $A=60^{\\circ}$, calculate the length of side $AC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1+\\sqrt{13}"
} | {
"split": "train",
"index": 27486,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has a right angle at $C$ , and $D$ is the foot of the altitude from $C$ to $AB$ . Points $L, M,$ and $N$ are the midpoints of segments $AD, DC,$ and $CA,$ respectively. If $CL = 7$ and $BM = 12,$ compute $BN^2$ . Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "193"
} | {
"split": "train",
"index": 27487,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A part of a book has fallen out. The number of the first fallen page is 387, and the number of the last page consists of the same digits but in a different order. How many sheets fell out of the book? Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "176"
} | {
"split": "train",
"index": 27488,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For what positive value of $t$ is $|{-4+ti}| = 2\\sqrt{13}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 27489,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression $1 - \\frac{1}{1 + \\sqrt{5}} + \\frac{1}{1 - \\sqrt{5}}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1 - \\frac{\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 27490,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a $7 \\times 7$ grid, choose $k$ cells such that the centers of any 4 chosen cells do not form the vertices of a rectangle. Find the maximum value of $k$ that satisfies this condition. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 27491,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given complex number $z$, define sequence $z_{0}, z_{1}, z_{2}, \\ldots$ as $z_{0}=z$ and $z_{n+1}=2 z_{n}^{2}+2 z_{n}$ for $n \\geq 0$. Given that $z_{10}=2017$, find the minimum possible value of $|z|$. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt[1024]{4035}-1}{2}"
} | {
"split": "train",
"index": 27492,
"solution": "Define $w_{n}=z_{n}+\\frac{1}{2}$, so $z_{n}=w_{n}-\\frac{1}{2}$, and the original equation becomes $$w_{n+1}-\\frac{1}{2}=2\\left(w_{n}-\\frac{1}{2}\\right)^{2}+2\\left(w_{n}-\\frac{1}{2}\\right)=2 w_{n}^{2}-\\frac{1}{2}$$ which reduces to $w_{n+1}=2 w_{n}^{2}$. i... |
deepscaler | [
{
"role": "user",
"content": "\nCompute the limit of the function:\n\n$$\n\\lim _{x \\rightarrow 0} \\frac{4^{5 x}-9^{-2 x}}{\\sin x-\\operatorname{tg}(x^{3})}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\ln (1024 \\cdot 81)"
} | {
"split": "train",
"index": 27493,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the value of:\n\\[3003 + \\frac{1}{3} \\left( 3002 + \\frac{1}{3} \\left( 3001 + \\dots + \\frac{1}{3} \\left( 4 + \\frac{1}{3} \\cdot 3 \\right) \\right) \\dotsb \\right).\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9006.5"
} | {
"split": "train",
"index": 27494,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the distinct prime factors of $7^7 - 7^4$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 27495,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $|\\overrightarrow {a}|=\\sqrt {2}$, $|\\overrightarrow {b}|=2$, and $(\\overrightarrow {a}-\\overrightarrow {b})\\bot \\overrightarrow {a}$, determine the angle between $\\overrightarrow {a}$ and $\\overrightarrow {b}$. Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 27496,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The operation $\\odot$ is defined as $a \\odot b = a + \\frac{3a}{2b}$. What is the value of $8 \\odot 6$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 27497,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Select 3 numbers from the range 1 to 300 such that their sum is exactly divisible by 3. How many such combinations are possible? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1485100"
} | {
"split": "train",
"index": 27498,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The first term of a sequence is $3107$. Each succeeding term is the sum of the squares of the digits of the previous term. What is the $614^{\\text{th}}$ term of the sequence? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 27499,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all values of $x$ that satisfy $x=1-x+x^{2}-x^{3}+x^{4}-x^{5}+\\cdots$ (be careful; this is tricky). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x=\\frac{-1+\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 27500,
"solution": "Multiplying both sides by $1+x$ gives $(1+x) x=1$, or $x=\\frac{-1 \\pm \\sqrt{5}}{2}$. However, the series only converges for $|x|<1$, so only the answer $x=\\frac{-1+\\sqrt{5}}{2}$ makes sense."
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest positive integer $n$ such that there exist $n$ distinct positive integers $x_{1}, x_{2}, \\cdots, x_{n}$ satisfying\n$$\nx_{1}^{2}+x_{2}^{2}+\\cdots+x_{n}^{2}=2017.\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 27501,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two fair, six-sided dice are rolled. What is the probability that the sum of the two numbers showing is less than or equal to 10 and at least one die shows a number greater than 3? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 27502,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the remainder when $2^{2^{2^2}}$ is divided by $500$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "536"
} | {
"split": "train",
"index": 27503,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sides opposite to the internal angles $A$, $B$, and $C$ of $\\triangle ABC$ are $a$, $b$, and $c$ respectively. It is given that $b\\sin C + c\\sin B = 4a\\sin B\\sin C$ and $b^2 + c^2 - a^2 = 8$. The area of $\\triangle ABC$ is __________. Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 27504,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose there are 100 cookies arranged in a circle, and 53 of them are chocolate chip, with the remainder being oatmeal. Pearl wants to choose a contiguous subsegment of exactly 67 cookies and wants this subsegment to have exactly \\(k\\) chocolate chip cookies. Find the sum of... | math | {
"style": "rule",
"ground_truth": "71"
} | {
"split": "train",
"index": 27505,
"solution": "We claim that the only values of \\(k\\) are 35 and 36. WLOG assume that the cookies are labelled 0 through 99 around the circle. Consider the following arrangement: cookies 0 through 17,34 through 50, and 67 through 84 are chocolate chip, and the remaining are oat... |
deepscaler | [
{
"role": "user",
"content": "8 people are seated in two rows with 4 people in each row. Among them, 2 specific people must sit in the front row, and 1 specific person must sit in the back row. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5760"
} | {
"split": "train",
"index": 27506,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the probability that two people, A and B, randomly choosing their rooms among 6 different rooms in a family hotel, which has two rooms on each of the three floors, will stay in two rooms on the same floor? Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"split": "train",
"index": 27507,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define the operation $a\\nabla b = 2 + b^a$. What is the value of $(1\\nabla 2) \\nabla 3$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "83"
} | {
"split": "train",
"index": 27508,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all $x$ such that $x^2+5x<6$. Express your answer in interval notation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(-6, 1)"
} | {
"split": "train",
"index": 27509,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the constant term in the expansion of $(x-2+ \\frac {1}{x})^{4}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 27510,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $p$ be a polynomial with integer coefficients such that $p(15)=6$ , $p(22)=1196$ , and $p(35)=26$ . Find an integer $n$ such that $p(n)=n+82$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 27511,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $y=(\\log_23)(\\log_34)\\cdots(\\log_n[n+1])\\cdots(\\log_{31}32)$ then Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y=5"
} | {
"split": "train",
"index": 27512,
"solution": "1. **Understanding the Product of Logarithms**:\n The expression for $y$ is given as a product of logarithms:\n \\[\n y = (\\log_2 3)(\\log_3 4) \\cdots (\\log_{31} 32).\n \\]\n Each term in the product is of the form $\\log_a b$, where $a$ and $b$ are co... |
deepscaler | [
{
"role": "user",
"content": "If \\(\\sum_{n = 0}^{\\infty} \\cos^{2n} \\theta = \\frac{9}{2}\\), what is the value of \\(\\cos{4\\theta}\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{31}{81}"
} | {
"split": "train",
"index": 27513,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a rectangle $P Q R S$ with $P Q=5$ and $Q R=3$, $P R$ is divided into three segments of equal length by points $T$ and $U$. What is the area of quadrilateral $S T Q U$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 27514,
"solution": "Since $P Q R S$ is a rectangle, then $P Q$ is perpendicular to $Q R$. Therefore, the area of $\\triangle P Q R$ is $\\frac{1}{2}(P Q)(Q R)=\\frac{1}{2}(5)(3)=\\frac{15}{2}$. Since $P T=T U=U R$, then the areas of $\\triangle P T Q, \\triangle T U Q$ and $\\triangle... |
deepscaler | [
{
"role": "user",
"content": "If the complex number \\( z \\) satisfies \\( |z| = 2 \\), then the maximum value of \\( \\frac{\\left|z^{2}-z+1\\right|}{|2z-1-\\sqrt{3}i|} \\) is _______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 27515,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ and $S_{1}$ respectively be the midpoints of edges $AD$ and $B_{1}C_{1}$. A rotated cube is denoted by $A^{\\prime}B^{\\prime}C^{\\prime}D^{\\prime}A_{1}^{\\prime}B_{1}^{\\prime}C_{1}^{\\prime}D_{1}^{\\prime}$. The common part of the original cube and the rotated one is... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} - \\frac{2}{3}"
} | {
"split": "train",
"index": 27516,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 10 sheikhs each with a harem of 100 wives standing on the bank of a river along with a yacht that can hold $n$ passengers. According to the law, a woman must not be on the same bank, on the yacht, or at any stopover point with a man unless her husband is present. What... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 27517,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $8 \\cdot 2^x = 5^{y + 8}$, then when $y = -8$, $x =$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 27518,
"solution": "1. **Substitute $y = -8$ into the equation:** \n Given the equation $8 \\cdot 2^x = 5^{y + 8}$, substituting $y = -8$ yields:\n \\[\n 8 \\cdot 2^x = 5^{-8 + 8}\n \\]\n Simplifying the exponent on the right-hand side:\n \\[\n 8 \\cdot 2^x = 5^0\n \\... |
deepscaler | [
{
"role": "user",
"content": "Compute $$2 \\sqrt{2 \\sqrt[3]{2 \\sqrt[4]{2 \\sqrt[5]{2 \\cdots}}}}$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2^{e-1}"
} | {
"split": "train",
"index": 27519,
"solution": "Taking the base 2 logarithm of the expression gives $$1+\\frac{1}{2}\\left(1+\\frac{1}{3}\\left(1+\\frac{1}{4}(1+\\cdots)\\right)\\right)=1+\\frac{1}{2!}+\\frac{1}{3!}+\\frac{1}{4!}+\\cdots=e-1$$ Therefore the expression is just $2^{e-1}$."
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x)=2x+1$. Find the sum of all $x$ that satisfy the equation $f^{-1}(x)=f(x^{-1})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 27520,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of \\( \\frac{5-2}{2+1} \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 27521,
"solution": "Simplifying, \\( \\frac{5-2}{2+1}=\\frac{3}{3}=1 \\)."
} |
deepscaler | [
{
"role": "user",
"content": "Find $x$, where $x$ is a square number which is divisible by four, and between 39 and 80. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 27522,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the sequence $\\{x_n\\}$ be defined by $x_1 \\in \\{5, 7\\}$ and, for $k \\ge 1, x_{k+1} \\in \\{5^{x_k} , 7^{x_k} \\}$ . For example, the possible values of $x_3$ are $5^{5^5}, 5^{5^7}, 5^{7^5}, 5^{7^7}, 7^{5^5}, 7^{5^7}, 7^{7^5}$ , and $7^{7^7}$ . Determine the s... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"split": "train",
"index": 27523,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the value of cos $$\\frac {π}{11}$$cos $$\\frac {2π}{11}$$cos $$\\frac {3π}{11}$$cos $$\\frac {4π}{11}$$cos $$\\frac {5π}{11}$$\\=\\_\\_\\_\\_\\_\\_． Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {1}{32}"
} | {
"split": "train",
"index": 27524,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Twenty-five cards are randomly arranged in a grid. Five of these cards have a 0 on one side and a 1 on the other side. The remaining twenty cards either have a 0 on both sides or a 1 on both sides. Loron chooses one row or one column and flips over each of the five cards in tha... | math | {
"style": "rule",
"ground_truth": "9:16"
} | {
"split": "train",
"index": 27525,
"solution": "The given arrangement has 14 zeroes and 11 ones showing. Loron can pick any row or column in which to flip the 5 cards over. Furthermore, the row or column that Loron chooses can contain between 0 and 5 of the cards with different numbers on their two sides. Of the... |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be a positive integer. Given that $n^{n}$ has 861 positive divisors, find $n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 27526,
"solution": "If $n=p_{1}^{\\alpha_{1}} p_{2}^{\\alpha_{2}} \\ldots p_{k}^{\\alpha_{k}}$, we must have $\\left(n \\alpha_{1}+1\\right)\\left(n \\alpha_{2}+1\\right) \\ldots\\left(n \\alpha_{k}+1\\right)=861=3 \\cdot 7 \\cdot 41$. If $k=1$, we have $n \\mid 860$, and the only pri... |
deepscaler | [
{
"role": "user",
"content": "Alice's favorite number has the following properties:\n\n\n- It has 8 distinct digits.\n- The digits are decreasing when read from left to right.\n- It is divisible by 180.\n\nWhat is Alice's favorite number?\n\n*Author: Anderson Wang* Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "97654320"
} | {
"split": "train",
"index": 27527,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfying $|\\overrightarrow{a}|=2$, $|\\overrightarrow{b}|=\\overrightarrow{a}\\cdot\\overrightarrow{b}=1$, and $(\\overrightarrow{a}-2\\overrightarrow{c}) \\cdot (\\overrightarrow{b}-\\overrightarrow{c})=0$, find ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{7}-\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 27528,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify: $i^0+i^1+\\cdots+i^{2009}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1 + i"
} | {
"split": "train",
"index": 27529,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain shopping mall sells two types of products, A and B. The profit margin for each unit of product A is $40\\%$, and for each unit of product B is $50\\%$. When the quantity of product A sold is $150\\%$ of the quantity of product B sold, the total profit margin for selli... | math | {
"style": "rule",
"ground_truth": "47.5\\%"
} | {
"split": "train",
"index": 27530,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many values of the digit $A$ is it true that $63$ is divisible by $A$ and $273{,}1A2$ is divisible by $4$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 27531,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P$ be the portion of the graph of $$ y=\\frac{6x+1}{32x+8} - \\frac{2x-1}{32x-8} $$ located in the first quadrant (not including the $x$ and $y$ axes). Let the shortest possible distance between the origin and a point on $P$ be $d$ . Find $\\lfloor 1000d \\rflo... | math | {
"style": "rule",
"ground_truth": "433"
} | {
"split": "train",
"index": 27532,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the number line, points $M$ and $N$ divide $L P$ into three equal parts. What is the value at $M$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{9}"
} | {
"split": "train",
"index": 27533,
"solution": "The difference between $\\frac{1}{6}$ and $\\frac{1}{12}$ is $\\frac{1}{6}-\\frac{1}{12}=\\frac{2}{12}-\\frac{1}{12}=\\frac{1}{12}$, so $L P=\\frac{1}{12}$. Since $L P$ is divided into three equal parts, then this distance is divided into three equal parts, each eq... |
deepscaler | [
{
"role": "user",
"content": "A square piece of paper has sides of length $100$. From each corner a wedge is cut in the following manner: at each corner, the two cuts for the wedge each start at a distance $\\sqrt{17}$ from the corner, and they meet on the diagonal at an angle of $60^{\\circ}$ (see the figu... | math | {
"style": "rule",
"ground_truth": "871"
} | {
"split": "train",
"index": 27534,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ that satisfy the conditions: $|\\overrightarrow{a}| = 2$, $|\\overrightarrow{b}| = \\sqrt{2}$, and $\\overrightarrow{a}$ is perpendicular to $(2\\overrightarrow{b} - \\overrightarrow{a})$, find the angle between $\\o... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 27535,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many six-digit numbers exist that have three even and three odd digits? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "281250"
} | {
"split": "train",
"index": 27536,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Lucky Larry's teacher asked him to substitute numbers for $a$, $b$, $c$, $d$, and $e$ in the expression $a-(b-(c-(d+e)))$ and evaluate the result. Larry ignored the parentheses but added and subtracted correctly and obtained the correct result by coincidence. The numbers Larry ... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 27537,
"solution": "1. **Substitute the given values into the expression ignoring parentheses:** \n Larry ignored the parentheses, so he calculated the expression as:\n \\[\n a - b - c - d + e = 1 - 2 - 3 - 4 + e\n \\]\n Simplifying this, we get:\n \\[\n -8 + e\n \\]\... |
deepscaler | [
{
"role": "user",
"content": "A line of soldiers 1 mile long is jogging. The drill sergeant, in a car, moving at twice their speed, repeatedly drives from the back of the line to the front of the line and back again. When each soldier has marched 15 miles, how much mileage has been added to the car, to the ... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 27538,
"solution": "30."
} |
deepscaler | [
{
"role": "user",
"content": "Andrew's grandfather's age is twelve times Andrew's age. If Andrew's grandfather was 55 years old when Andrew was born, how many years old is Andrew now? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 27539,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point $Q$ is chosen at random in the interior of equilateral triangle $DEF$. What is the probability that $\\triangle DEQ$ has a greater area than each of $\\triangle DFQ$ and $\\triangle EFQ$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 27540,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Medians $\\overline{DP}$ and $\\overline{EQ}$ of $\\triangle DEF$ are perpendicular. An altitude $\\overline{ER}$ from $E$ to line $DF$ is such that $ER = 15$. Given $DP= 27$ and $EQ = 36$, determine the length of ${DF}$. Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 27541,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In Ms. Johnson's class, each student averages two days absent out of thirty school days. What is the probability that out of any three students chosen at random, exactly two students will be absent and one will be present on a Monday, given that on Mondays the absence rate incr... | math | {
"style": "rule",
"ground_truth": "1.5\\%"
} | {
"split": "train",
"index": 27542,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the numbers \\\\(1\\\\), \\\\(2\\\\), \\\\(3\\\\), \\\\(4\\\\), \\\\(5\\\\), \\\\(6\\\\), two numbers are selected to form an ordered pair of real numbers \\\\((x, y)\\\\). The probability that \\\\(\\dfrac{x}{y+1}\\\\) is an integer is equal to \\_\\_\\_\\_\\_\\_ Let's th... | math | {
"style": "rule",
"ground_truth": "\\dfrac{4}{15}"
} | {
"split": "train",
"index": 27543,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The values of a function $f(x)$ are given in the table below.\n\n\\begin{tabular}{|c||c|c|c|c|c|} \\hline $x$ & 1 & 2 & 3 & 4 & 5 \\\\ \\hline $f(x)$ & 3 & 1 & 5 & 4 & 2 \\\\ \\hline\n\\end{tabular}If $f^{-1}$ exists, then what is $f^{-1}(f^{-1}(f^{-1}(1)))$? Let's think step b... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 27544,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$(1)$ If $A=\\frac{a-1}{a+2}•\\frac{{a}^{2}-4}{{a}^{2}-2a+1}÷\\frac{1}{a-1}$, simplify $A$;<br/>$(2)$ If $a$ satisfies $a^{2}-a=0$, find the value of $A$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 27545,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many non- empty subsets $S$ of $\\{1,2,3,\\ldots ,15\\}$ have the following two properties?\n$(1)$ No two consecutive integers belong to $S$.\n$(2)$ If $S$ contains $k$ elements, then $S$ contains no number less than $k$. Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "405"
} | {
"split": "train",
"index": 27546,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Aaron has 144 identical cubes, each with edge length 1 cm. He uses all of the cubes to construct a solid rectangular prism, which he places on a flat table. If the perimeter of the base of the prism is 20 cm, what is the sum of all possible heights of the prism? Let's think ste... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 27547,
"solution": "Suppose that the base of the prism is $b \\mathrm{~cm}$ by $w \\mathrm{~cm}$ and the height of the prism is $h \\mathrm{~cm}$. Since Aaron has 144 cubes with edge length 1 cm, then the volume of the prism is $144 \\mathrm{~cm}^{3}$, and so $bwh = 144$. Since the pe... |
deepscaler | [
{
"role": "user",
"content": "The area of the enclosed shape formed by the line $y=0$, $x=e$, $y=2x$, and the curve $y= \\frac {2}{x}$ is $\\int_{1}^{e} \\frac{2}{x} - 2x \\,dx$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "e^{2}-3"
} | {
"split": "train",
"index": 27548,
"solution": ""
} |
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