prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 38/3 |
[
{
"content": "Determine whether the complete graph $K_8$ can be embedded on a torus without any edges crossing.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.55 m |
[
{
"content": "Calculate the volume of the solid enclosed by the surfaces $z = x^2$ and $z = 4 - x^2 - y^2$. The projection of the solid onto the $xy$-plane is an ellipse given by the equation $\\frac{x^2}{2} + \\frac{y^2}{4} = 1$. Express the volume $V$ as an integral and evaluate it.",
"role": "user"
}
] | 4\sqrt{2}\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | {eq}\text{Break-even point} = \dfrac{\text{Fixed Costs}}{\text{Contribution Margin%}}{/eq} |
[
{
"content": "Let $F$ be a field with $5^{12}$ elements. Determine the total number of proper subfields of $F$. Provide your answer as a single integer.",
"role": "user"
}
] | 5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.6 atm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 102.35% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $28286.11 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{t \\to 1} \\frac{\\sqrt{2t^2-1}\\sqrt[3]{4t^3-3t}-1}{t^2-1} \\]",
"role": "user"
}
] | \dfrac{5}{2} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\rightarrow \\infty} (e^{2x}+x)^{1/x} \\]",
"role": "user"
}
] | e^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 170 m/s |
[
{
"content": "Determine whether the following statement is true or false: Let $R$ be a commutative ring and $I$ be an ideal of $R$. $I$ is a principal ideal if and only if $I$ is a free $R$-module.",
"role": "user"
}
] | B |
[
{
"content": "Does Taylor's theorem with the Lagrange remainder hold when the roles of \\( a \\) and \\( b \\) are reversed? Specifically, if \\( f \\) is \\( \\mathcal{C}^n([a,b]) \\) and \\( n+1 \\) times differentiable, can we find a \\( c \\in (a,b) \\) such that:\n\\[ f(a) = f(b) + f'(b)(a-b) + \\dots + \\... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.0940 |
[
{
"content": "Evaluate the limit: $$ \\lim_{x\\to-∞} \\left(\\sqrt{x^2-\\sqrt{x^2+1}}+x\\right) $$",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "Given that \\( \\sin\\theta = \\frac{\\sqrt{4-x}}{\\sqrt{2}} \\), find an expression for \\( \\cos 4\\theta \\) without using trigonometric identities.",
"role": "user"
}
] | 2x^2 - 12x + 17 |
[
{
"content": "Evaluate the integral \\( \\int_{|z| = 1}\\frac{1}{(1-3z)(1-2z)^2}dz \\) using the residue theorem, where \\( z \\) is a complex number.",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.3e-19 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.5e-13 J |
[
{
"content": "Let $R$ be a commutative ring with unity and $I$ be an ideal of $R$. Determine whether $\\text{Hom}_R(R/I, R/I) \\cong R/I$ as $R$-modules.",
"role": "user"
}
] | R/I |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 164.69 g |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\frac{x}{x^2+1}\\sin(ax)\\,dx \\) using complex analysis techniques.",
"role": "user"
}
] | \pi \operatorname{sgn}(a) e^{-|a|} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.096 MeV |
[
{
"content": "Suppose $E_1$ and $E_2$ are elliptic curves given by $y^2 = 4x^3 + A_ix + B_i$ for $i=1,2$, where $A_i, B_i \\in \\mathbb{C}$ are algebraic over $\\mathbb{Q}$. Let $\\Lambda_1$ and $\\Lambda_2$ be the unique lattices parametrizing $E_1$ and $E_2$, respectively, such that $g_2(\\Lambda_i) = A_i$ an... | Yes |
[
{
"content": "Evaluate the surface integral of the vector field $\\mathbf{F}(x, y, z) = \\left(\\frac{1}{x}, \\frac{1}{y}, \\frac{1}{z}\\right)$ over a sphere $S$ of radius $R$ with outward orientation.",
"role": "user"
}
] | 12\pi R |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 385 W |
[
{
"content": "Find a 5-cycle $x$ such that $x^3 = (abcde)$. Show your work and verify that $x^3$ equals $(abcde)$. What is the 5-cycle $x$?",
"role": "user"
}
] | (a\,c\,e\,b\,d) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | referent power |
[
{
"content": "Evaluate the limit \\( \\lim_{x \\to 0} \\frac{\\ln(1 - \\sin x) + x}{x^2} \\) without using l'Hôpital's rule.",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 13.50m/s^2 |
[
{
"content": "Let $R$ be the ring $\\mathbb{Z}[x]/((x^2+x+1)(x^3 +x+1))$ and $I$ be the ideal generated by $2$ in $R$. Determine the cardinality of the ring $R/I$. \\( \\boxed{?} \\)",
"role": "user"
}
] | 32 |
[
{
"content": "Does the statement \"If a characteristic function \\( \\varphi \\) is integrable \\( (\\varphi \\in L^{1}) \\), then there is a continuous bounded density function \\( f(x) = \\frac{1}{2\\pi}\\int_{\\mathbb{R}}\\exp(-itx)\\varphi(t)dt \\; \\forall x \\in \\mathbb{R} \\)\" imply that if \\( \\mathb... | Yes |
[
{
"content": "Find the point \\( O \\) such that the sum of the distances from \\( O \\) to the points \\( A, B, C, \\) and \\( D \\) is minimized.",
"role": "user"
}
] | O |
[
{
"content": "As a prank, Tim decides to steal Nathan's fork at dinner, but so he doesn't get caught, he convinces other people to do it for him. On Monday, he convinces Joe to do it. On Tuesday, he could get either Ambie or John to do it. On Wednesday, he can't convince any of those three people to do it, but ... | 40 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | ```java
import java.time.LocalTime;
import java.time.Duration;
public class Clock {
private LocalTime startTime;
private LocalTime stopTime;
public Clock() {
startTime = LocalTime.now();
}
public void start(String start) {
startTime = parse(start);
}
public void start() {... |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 16.9 m |
[
{
"content": "Evaluate the integral \\(\\int_C (z+\\bar{z})^3\\,dz\\) where \\(C\\) is the unit circle.",
"role": "user"
}
] | 6\pi i |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 804274 |
[
{
"content": "If $\\mathbf{a},$ $\\mathbf{b},$ and $\\mathbf{c}$ are unit vectors, then find the largest possible value of\n\\[\\|\\mathbf{a} - \\mathbf{b}\\|^2 + \\|\\mathbf{a} - \\mathbf{c}\\|^2 + \\|\\mathbf{b} - \\mathbf{c}\\|^2.\\]Note: A unit vector is a vector of magnitude 1.",
"role": "user"
}
] | 9 |
[
{
"content": "Compute the residue of the function \\( \\frac{z^2 + 3z - 1}{z+2} \\) at the pole \\( z = -2 \\).",
"role": "user"
}
] | -3 |
[
{
"content": "Given the joint probability distribution \\( f(x,y) = \\begin{cases} xe^{-x-y}, & x,y>0 \\\\ 0, & \\text{elsewhere} \\end{cases} \\), compute the probability \\( P(X \\le Y) \\).",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Let $p(z)$ be a polynomial of degree 2 satisfying the following conditions:\n\\[ \\frac{1}{2\\pi i}\\int_{|z|=2}\\frac{zp'(z)}{p(z)}dz = 0 \\text{ and } \\frac{1}{2\\pi i}\\int_{|z|=2}\\frac{z^2p'(z)}{p(z)}dz = -2. \\]\nIf $p(0) = 2017$, find the explicit form of $p(z)$. Use the Argument Principle... | 2017(z^2 + 1) |
[
{
"content": "Determine whether the function $f: \\mathbb{R}^m \\rightarrow \\mathbb{R}$, defined by the condition $|f(y)| \\leq |y|^3$, is differentiable at the origin. Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the coefficient of \\(x^{33}\\) in the expansion of \\((x+x^3)(1+5x^6)^{-13}(1-8x^9)^{-37}\\).",
"role": "user"
}
] | 83019300 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | THOME COMPANY
Manufacturing Overhead Flexible Budget Report
For the Month Ended July 31, 2014
| Costs | Budget | Actual Costs | Difference |
|---|---|---|---|
| Variable Costs | | | |
| Indirect Labor | $12,240 | $11,959 | $281 F |
| Indirect Materials | $9,180 | $9,001 | $179 U |
| Utilities | $4,080 | $3,665 | $415... |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.32 mL |
[
{
"content": "In a scalene triangle \\( ABC \\), one angle equals the difference between the other two angles, and one angle is twice another angle. The angle bisectors of angles \\( A \\), \\( B \\), and \\( C \\) intersect the circumcircle of the triangle at points \\( L \\), \\( O \\), and \\( M \\) respecti... | 44 |
[
{
"content": "Let $a, b, c$ be positive real numbers such that $a + 2b + 3c = 26$ and $a^2 + b^2 + c^2 = 52$. Find the largest possible value of $a$. Use the Cauchy-Schwarz inequality to verify your result.",
"role": "user"
}
] | \dfrac{26}{7} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | v=(BId/m)t |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Output (Suits Cleaned) Price per Suit ($) Total Costs ($) Total Revenue ($) MC ($) MR($)0 14.00 3.00 - - -1 13.50 6.00 13.50 3.00 13.502 13.00 8.50 26.00 2.50 12.503 12.50 10.50 37.50 2.00 11.504 12.00 11.50 48.00 1.00 10.505 11.50 13.50 57.50 2.00 9.506 11.00 22.00 66.00 8.50 8.507 10.50 30.00 73.50 8.00 7.508 10.0... |
[
{
"content": "Construct an explicit deformation retraction of \\(\\mathbb{R}^n - \\{0\\}\\) onto \\(S^{n−1}\\). Consider the homotopy given by:\n\\[ f_t(x) = (1-t)x + t \\frac{x}{|x|}, \\quad t \\in [0,1], \\]\nwhere \\(f_0(x) = x\\) and \\(f_1(x) = \\frac{x}{|x|}\\). Show that this defines a deformation retrac... | f_t(x) = (1 - t)x + t \frac{x}{|x|} |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} \\left| \\sin \\left( \\frac{\\pi}{2(n+1)} \\right) \\right|^{2n+1} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.138e-14 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.93 A |
[
{
"content": "Let $H$ be a Hilbert space and $X$ be a subset of $H$. If $X$ is connected and compact, is $X$ necessarily path-connected?",
"role": "user"
}
] | No |
[
{
"content": "Does the poset of free factors of a free group form a lattice? Specifically, for a free group $F_n$ of rank $n$, is the set of its free factors, partially ordered by inclusion, a lattice?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the minimum number of nails required to fix any convex polygon on a table, where nails can touch the boundary but not pass through the polygon.",
"role": "user"
}
] | 3 |
[
{
"content": "Given the functional equation \\( f(z) = z + f(z^2) \\), express it in terms of the coefficients of the power series \\( f(z) = \\sum_{j=0}^\\infty a_j z^j \\). Determine the radius of convergence of the resulting series.",
"role": "user"
}
] | 1 |
[
{
"content": "A store carries chocolate, vanilla, peppermint, and lemon candies. One day, the store clerk notices that he has fifteen candies total. Furthermore, the number of peppermint and lemon candies together is twice the number of chocolate and vanilla candies together, and there are eight more peppermint... | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -1 cm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | \vec{\mu}=F\pi q \dfrac{L^2}{12}\;\hat{n} |
[
{
"content": "Determine the radius of convergence of the series \\( \\sum_{n=1}^\\infty \\frac{2^n x^{n!}}{n} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 37 N/C |
[
{
"content": "Let $\\alpha$ and $\\beta$ be two complex numbers with $\\beta$ non-zero. Suppose $f(z)$ is a polynomial function on $\\mathbb{C}$ such that $f(z)=\\alpha$ whenever $z^{5}=\\beta$. What is the degree of $f(z)$?",
"role": "user"
}
] | 5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Project P1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The wavelength is equal to the velocity of the wave (the speed of light) divided by the frequency of the wave. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.11 m |
[
{
"content": "Determine whether there exists an automorphism \\( f : \\mathcal{M}_{3} ( \\mathbb{C} ) \\to \\mathcal{M}_{3} ( \\mathbb{C} ) \\) of \\( \\mathbb{C} \\)-algebras such that \\( f^3 ( M ) = M \\) for all matrices \\( M \\). If such an automorphism exists, describe how to construct it.",
"role": ... | Yes |
[
{
"content": "Determine the number of ways to select 13 cards from a standard 52-card deck such that each rank from 2 to A appears exactly once and no two cards of the same suit have consecutive ranks, including A and 2 as consecutive.",
"role": "user"
}
] | 1594320 |
[
{
"content": "Given a triangle \\(ABC\\), it is known that for any point \\(M\\) inside the triangle \\(ABC\\), a triangle can be formed using the three segments \\(MA\\), \\(MB\\), and \\(MC\\). Determine if the triangle \\(ABC\\) must be equilateral.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $58.50 |
[
{
"content": "Find the limit: $$\\lim_{n \\to \\infty} \\underbrace{\\sin \\sin \\ldots \\sin }_{\\text{$n$ times}}x$$",
"role": "user"
}
] | 0 |
[
{
"content": "Find the coefficient of the term $x^3y^4z^5$ in the expansion of the polynomial $(x + y + z)^8(x + y + z + 1)^8$. Provide your answer as a single number.",
"role": "user"
}
] | 1940400 |
[
{
"content": "Let $R$ be an integral domain, and let $a, b \\in R$ with $a \\neq 0$ and $b \\neq 0$. Given that $15a = 0$ and $3b \\neq 0$, determine the characteristic of $R$.",
"role": "user"
}
] | 5 |
[
{
"content": "Factor the expression $x(x+2)+(x+2)$.",
"role": "user"
}
] | (x+1)(x+2) |
[
{
"content": "Evaluate the limit using L'Hôpital's rule: $$\\lim_{x\\to0}\\frac{e^{-\\frac{1}{x^2}}}{x}$$",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $29,868 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Ice Cream Cones | Total Utility | Marginal Utility
---|---|---
0 | 0 | 0
1 | 12 | 12
2 | 22 | 10
3 | 31 | 9
4 | 39 | 8
5 | 45 | 6
6 | 50 | 5
7 | 52 | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12.35 m/s |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0}\\frac{1}{x^2} \\int_{0}^{x^2}f(y)dy$$ where $f(x)$ is a continuous function on $\\mathbb{R}$ and $\\lim_{x \\to 0}f(x)=a$. Find the value of the limit.",
"role": "user"
}
] | a |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $15,670 |
[
{
"content": "Determine whether there are infinitely many Fibonacci numbers that are also powers of 2. If not, find the largest Fibonacci number that is a power of 2.",
"role": "user"
}
] | 8 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -$2800 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 164 N |
[
{
"content": "Calculate the limit \\(\\lim_{n\\to \\infty} \\frac{1}{n} \\int_0^n f(x) \\, dx\\) given that \\(f: \\mathbb{R} \\to (0, \\infty)\\) is continuous and satisfies \\(\\lim_{x\\to \\infty}\\frac{f(x)}{f(x+1)}=0.\\)",
"role": "user"
}
] | \infty |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 129.7477*10^-12*a^3 |
[
{
"content": "Find the value of $k$ for which the integral \\( \\int_{0}^{1} \\frac{\\ln(x)}{x^k} \\, dx \\) has a finite value.",
"role": "user"
}
] | k < 1 |
[
{
"content": "Define the sequence \\(x_{i}\\) by \\(x_{1}=a\\) and \\(x_{i+1}=2x_{i}+1\\). Define the sequence \\(y_{i}=2^{x_{i}}-1\\). Find the largest integer \\(k\\) such that \\(y_{1}, \\ldots, y_{k}\\) are all prime numbers.",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 78.4% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.415 |
[
{
"content": "For fixed values $0 < a_1 \\leq a_2 \\leq a_3$, find the positive value of $x$ that minimizes the function \\( g(x) = \\max_{1\\leq i \\leq 3} \\left(\\frac{a_i - x}{a_i + x}\\right)^2 \\).",
"role": "user"
}
] | \sqrt{a_1 a_3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | V(t) = (2V_0/T)t |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $36,952.70 |
[
{
"content": "Evaluate the integral \\( \\int_D \\frac{4x 4y 4z}{x^2} \\, dxdydz \\), where the domain \\( D \\) is defined as \\( D=\\{(x, y,z) \\in \\mathbb{R}^3 \\mid x,z \\in [1,e], \\ 0\\le y\\le\\sqrt{\\ln z}\\} \\).",
"role": "user"
}
] | 8(e^2 + 1) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Tensile stress |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $2,250 |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} n^2 \\int_{n}^{5n}\\frac{x^3}{1+x^6}dx \\).",
"role": "user"
}
] | \dfrac{12}{25} |
[
{
"content": "Find the residue of the function \\( \\frac{z}{z^6+1} \\) at the point \\( z=i \\).",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"content": "Find the arc length of the curve defined by the vector function \\( r(t) = ti + j + \\left(\\frac{1}{6}t^3 + \\frac{1}{2}t^{-1}\\right)k \\) from \\( t=0 \\) to \\( t=2 \\).",
"role": "user"
}
] | \infty |
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