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... | 48.2 |
[
{
"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... | Timeliness |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{1}{2n}\\log\\binom{2n}{n} \\]",
"role": "user"
}
] | \log 2 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^\\infty \\frac{x\\sin(x)}{x^2+a^2} \\, dx \\) using a complex contour integral, where \\( a > 0 \\).",
"role": "user"
}
] | \pi 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... | 1,124.08 |
[
{
"content": "Evaluate the limit of \\( g(r,\\theta)= \\frac{r^2(\\cos\\theta-\\sin\\theta)^2}{|\\cos\\theta|+|\\sin\\theta|} \\) as \\((r,\\theta)\\) approaches \\((0,0)\\).",
"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... | 45.258 N |
[
{
"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... | 5.08% |
[
{
"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... | 571.4 nm, 444.4 nm, 363.6 nm |
[
{
"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... | 1237.6 N |
[
{
"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... | Mg+Mn_2O_3 -> MgO+2MnO |
[
{
"content": "Calculate the angle between the line \\((6, 8, 5) + t (3, 4, 5)\\), where \\(t \\in \\mathbb{R}\\), and the sphere \\(x^2 + y^2 + z^2 = 25\\) at their points of intersection.",
"role": "user"
}
] | 45^\circ |
[
{
"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... | 90% |
[
{
"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... | $16,047,160 |
[
{
"content": "Given two independent and identically distributed random variables $X$ and $Y$ with moment generating function \\( M(t) = \\left( \\frac{1}{1-1.5t}\\right)^2 \\) for \\( t < \\frac{2}{3} \\), calculate the standard deviation of the sum $X + Y$. Assume $X$ and $Y$ are Erlang distributed.",
"rol... | 3 |
[
{
"content": "Find the largest integer \\( m \\) such that \\( 2^m \\) divides \\( 3^{2n+2} - 8n - 9 \\) for natural numbers \\( n \\).",
"role": "user"
}
] | 6 |
[
{
"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... | 1.318e-3 M |
[
{
"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... | 280 s |
[
{
"content": "Determine the curvature of the cycloid defined by the parametric equations \\( x = t - \\sin(t) \\) and \\( y = 1 - \\cos(t) \\) at the point where \\( t = 0 \\). Note that the standard curvature formula \\( \\kappa = \\frac{||\\det (r'(t), r''(t))||}{||r'(t)||^3} \\) cannot be applied directly at... | \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... | 2.91 m/s |
[
{
"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... | 7 m |
[
{
"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... | 643*10^-6 m^3/s |
[
{
"content": "Find the set of values of $x$ such that the inequality \\((a^2-1)x^2+(3-2a)x-1>0\\) holds for all values of $a$.",
"role": "user"
}
] | (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... | rate = 3.0e-5 [A]^2[B]^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... | decrease |
[
{
"content": "Evaluate the limit using Taylor expansions: $$ \\lim_{z \\to 0} \\frac{(1-\\cos z)^2}{(e^z-1-z)\\sin^2z} $$",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Compute the limit \\( \\lim_{x\\to0}{\\frac{e^{-1/x^2}}{x^2}} \\) without using L'Hopital's rule.",
"role": "user"
}
] | 0 |
[
{
"content": "Solve the differential equation \\(2yy' + 1 = y^2 + x\\) with the initial condition \\(y(0) = 1\\).",
"role": "user"
}
] | \sqrt{e^x - x} |
[
{
"content": "Let $ f : \\mathbb{R} \\to \\mathbb{R} $ be a continuous function such that $ f(x) f(f(x)) = 1 $. Given that $ f(1000) = 999 $, find the value of $ f(500) $. \\( \\text{(Express your answer as a single number.)} \\)",
"role": "user"
}
] | \dfrac{1}{500} |
[
{
"content": "Gavrila throws a ball from behind his head at a speed of $5 \\text{ m/s}$ against the wind at an angle to the horizontal. After 1 second, the ball hits his stomach 1 meter below the point of release. Given that the force exerted on the ball by the air is directed horizontally and does not depend o... | \dfrac{3}{4} |
[
{
"content": "Let $X_1$, $X_2$, and $X_3$ be independent, identically distributed continuous random variables from an Exponential Distribution. Find the probability that the median of $X_1$, $X_2$, and $X_3$ is closer to the smallest value $X_{(1)}$ than it is to the largest value $X_{(3)}$. Express your answer... | \dfrac{2}{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... | 125.075 N |
[
{
"content": "Find all positive integers $k$ for which there exist positive integers $n$ and $m$ (with $m \\ge 2$) such that $3^k + 5^k = n^m$.",
"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... | 9.3 |
[
{
"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... | $125 |
[
{
"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... | 7.88e-3 m^2 |
[
{
"content": "Determine the area of the largest irregular hexagon that can be inscribed in the ellipse given by the equation \\( \\frac{x^2}{16} + \\frac{y^2}{9} = 1 \\).",
"role": "user"
}
] | 18\sqrt{3} |
[
{
"content": "How many zeroes does $10!$ end in, when written in base 11?",
"role": "user"
}
] | 0 |
[
{
"content": "Find the volume of the solid region bounded by the paraboloids \\(z=2x^2+2y^2\\) and \\(z=3-x^2-y^2\\).",
"role": "user"
}
] | \dfrac{3\pi}{2} |
[
{
"content": "In a right triangle $ABC$ with $\\angle CBA = 90^\\circ$, point $D$ is the midpoint of $[BC]$. The angle $\\angle BAD = 2\\angle DAC = 2\\alpha$. Point $E$ is on $[AD]$ such that $\\angle BED = 90^\\circ$ and $|DE| = 3$. Determine the length of $|AB| = x$. \\( \\boxed{x} \\)",
"role": "user"
... | 6 |
[
{
"content": "In triangle \\( PQR \\), points \\( N \\) and \\( L \\) are located on sides \\( PQ \\) and \\( PR \\) respectively, such that \\( NQ = LR \\). The intersection point \\( A \\) of segments \\( QL \\) and \\( NR \\) divides \\( QL \\) in the ratio \\( m:n \\) from point \\( Q \\). Determine the rat... | \dfrac{n}{m} |
[
{
"content": "Given the equation \\(z = (x+i)^2\\) where \\(x > 0\\) is a real number, and \\(\\arg(z) = \\frac{\\pi}{3}\\), solve for \\(x\\).",
"role": "user"
}
] | \sqrt{3} |
[
{
"content": "Let $h: \\mathbb{R}^3 \\rightarrow \\mathbb{R}$ be defined by $h(x,y,z)=g(x^2-y^2,y^2-z^2)$, where $g: \\mathbb{R}^2 \\rightarrow \\mathbb{R}$ is a differentiable function with $\\nabla g(0,0)=(1,2)$. Determine the directional derivative of $h$ at the point $(1,1,1)$ in the direction of the vector... | 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... | $254,243.78 |
[
{
"content": "Let $\\mathcal{H}$ be a Hilbert space, $B(\\mathcal{H})$ the bounded linear operators on $\\mathcal{H}$, and $M_n(B(\\mathcal{H}))$ the $n \\times n$ matrices with operator-valued entries. Consider a matrix $A = [a_{ij}]$ in $M_n(B(\\mathcal{H}))$. If $\\sum_{i,j=1}^n u_i^* a_{ij} u_j$ is a positi... | 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... | 37.56 kJ/mol |
[
{
"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... | 40% debt and 60% equity |
[
{
"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... | $9992.8 |
[
{
"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... | 9.5% |
[
{
"content": "Determine whether there exists a first-order logic formula, without using the identity operator, that can only be satisfied by infinite structures, assuming the structures are non-empty.",
"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... | C4H12N3 |
[
{
"content": "Evaluate the triple integral \\( \\iiint_B \\sqrt{x^2+y^2+z^2} \\, dV \\) over the region \\( B \\) in \\( \\mathbb{R}^3 \\) defined by the inequalities \\( 0 \\leq x \\), \\( 0 \\leq y \\), \\( 0 \\leq z \\), and \\( x^2 + y^2 + z^2 \\leq 4 \\). Express the integral in spherical coordinates and f... | 2\pi |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty} \\int_{1/n}^{1} \\frac{nx^{n-1}}{(x+1)^2}dx$$",
"role": "user"
}
] | \dfrac{1}{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... | 125108.14 |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\rightarrow \\infty}\\left(\\frac{\\pi}{2}-\\arctan n^2\\right)\\cdot \\ln n!$$",
"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... | 1.86 g/L |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to -\\frac{\\pi}{2}^+} \\frac{e^{\\tan x}}{\\ln \\left(\\frac{\\pi}{2}+x\\right)}$$",
"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... | 0.1 rad/sec |
[
{
"content": "Determine whether a topological space obtained as the countable product of topological spaces, each having a countable basis, also has a countable basis.",
"role": "user"
}
] | Yes |
[
{
"content": "In a finite-dimensional complex Hilbert space \\( \\mathcal{H} \\), is every isometric map also a symmetry transformation? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Given an integer \\( k \\), the function \\( f(n) \\) is defined on the set of negative integers and takes integer values. It satisfies the equation \\[ f(n)f(n+1)=(f(n)+n-k)^2, \\] for \\( n = -2, -3, \\ldots \\). Find an expression for \\( f(n) \\).",
"role": "user"
}
] | (n - k)^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... | $26,250 |
[
{
"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... | 2.604e-47 kg m^2 |
[
{
"content": "Calculate \\( \\lim\\limits_{x\\to 0}\\bigg(x^2\\bigg(1+2+3+\\ldots+\\bigg\\lfloor\\dfrac{1}{\\mid x\\mid}\\bigg\\rfloor\\bigg)\\bigg) \\).",
"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... | Direct Labor Hours 6,400 7,600 8,800 10,000
Variable Cost
Indirect Labor($1.10) $7,040 $8,360 $9,680 $11,000
Indirect materials ($0.70) $4,480 $5,320 $6,160 $7,000
Utilities ($0.20) $1,280 $1,520 $1,760 2,000
Total Variable Cost $12,800 $15,200 $17,600 $20,000
Fixed Cost
Supervision $4,000 $4,000 $4,000 $4,000
Depreciation $1,500 $1,500 $1,500 $1,500
Property Taxes $700 $700 $700 $700
Total Fixed Cost $6,200 $6,200 $6,200 $6,200
Total Cost $19,000 21400 $ 23,800 $26,200 |
[
{
"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... | Marketing plan |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^\\infty \\frac{e^{ix}}{x} \\, dx \\) using contour integration techniques. Verify if the result \\( I_0 = i\\pi \\) is correct.",
"role": "user"
}
] | i\pi |
[
{
"content": "Evaluate the sum \\( \\sum_{k=0}^n k \\binom{n}{k} p^k (1-p)^{n-k} \\), where \\( 0<p<1 \\).",
"role": "user"
}
] | np |
[
{
"content": "In triangle \\( \\triangle ABC \\), the sides opposite to angles \\( \\angle A \\), \\( \\angle B \\), and \\( \\angle C \\) are \\( a \\), \\( b \\), and \\( c \\) respectively. Given that:\n\\[ a^2 + 2(b^2 + c^2) = 2\\sqrt{2} \\]\nfind the maximum value of the area of triangle \\( \\triangle ABC... | \dfrac{1}{4} |
[
{
"content": "As point C moves along the upper arc of a circle with radius 1, centered at the origin (0, 0), from point A (-1, 0) to point B (1, 0), the angle BOC decreases at a constant rate of 1 radian per minute. Determine the rate of change of the area of triangle ABC, in square units per minute, at the ins... | \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... | 7.42e+30 kg |
[
{
"content": "Determine whether there always exists a subfield of \\(\\mathbb{C}\\) that serves as a splitting field for a polynomial \\(f(x) \\in \\mathbb{Q}[X]\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Let $p(x)$ be a polynomial with integer coefficients. Given that $p(a) = p(b) = p(c) = -1$ for three distinct integers $a$, $b$, and $c$, determine the number of integer roots of $p(x)$. Provide your answer as an integer.",
"role": "user"
}
] | 0 |
[
{
"content": "Find the value of \\( \\lim_{x \\to \\infty} \\left( \\frac{x+\\pi}{x+e} \\right)^x \\).",
"role": "user"
}
] | e^{\pi - e} |
[
{
"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... | 91476.366 Pa |
[
{
"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... | $40,900 |
[
{
"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... | 10.8 m/s |
[
{
"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... | 3265.3 |
[
{
"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... | 16.80% |
[
{
"content": "Determine the region of convergence for a Laurent series where the principal part converges for \\(|z| > 1\\) and the analytic part converges for \\(|z| < 2\\).",
"role": "user"
}
] | 1 < |z| < 2 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\sum_{i=1}^n \\frac{i^{1/i}}{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... | $379,435.35 |
[
{
"content": "Find all non-integer values of $x$ such that \\( x + \\frac{13}{x} = \\lfloor x \\rfloor + \\frac{13}{\\lfloor x \\rfloor} \\), where \\( \\lfloor x \\rfloor \\) denotes the greatest integer less than or equal to \\( x \\).",
"role": "user"
}
] | -\dfrac{13}{4} |
[
{
"content": "Let \\( F_{1}, F_{2}, F_{3}, \\ldots \\) be a sequence of convex quadrilaterals where \\( F_{k+1} \\) (for \\( k=1, 2, 3, \\ldots \\)) is obtained as follows: \\( F_{k} \\) is cut along a diagonal, one of the parts is flipped over, and then glued along the cut line with the other part. What is the... | 6 |
[
{
"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... | $3,577.41 |
[
{
"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... | -1667/4 |
[
{
"content": "Compute the limit \\( \\lim_{R \\to +\\infty} I(R) \\), where \\( I(R) = \\int_{\\gamma_R}(1+x_1^2+x_2^2)^{-1/2}\\cos(x_2)\\,ds \\) and \\( \\gamma_R \\) is the semi-circular arc with center at the origin and radius \\( R \\) in the first quadrant. Use the parameterization \\( x_1 = R\\cos\\phi, x... | 0 |
[
{
"content": "Do all unitary matrices, when squared, equal the identity matrix?",
"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... | -84% |
[
{
"content": "Evaluate the sum of the series: \\[ \\sum_{n=0}^\\infty \\frac{(-1)^{n+1}n}{(2n+1)!} \\cdot \\pi^{2n} \\]",
"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... | 6.04e+24 kg |
[
{
"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... | 7.40% |
[
{
"content": "Find the last two digits of the number $13^{101}$ when expressed in base 3 (ternary).",
"role": "user"
}
] | 21 |
[
{
"content": "Determine whether the domain \\( D = \\{f \\in L^2(\\mathbb{R}) : \\frac{d^2f}{dx^2} \\in L^2(\\mathbb{R})\\} \\) is dense in \\( L^2(\\mathbb{R}) \\). Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "If $f:\\mathbb{R}\\rightarrow \\mathbb{R}$ is a continuous, open surjection, is it necessarily a homeomorphism?",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the sum of the series: \\[ \\sum^{\\infty}_{n=1} (-1)^{n+1}\\frac{n-1}{(n-1)!} \\]",
"role": "user"
}
] | -\dfrac{1}{e} |
[
{
"content": "Evaluate the limit \\( \\lim\\limits_{n\\to\\infty} \\int_0^1 \\frac{x^n}{1+x^n} \\, dx. \\)",
"role": "user"
}
] | 0 |
[
{
"content": "Suppose $R$ is a commutative ring such that for every ascending chain of ideals $I_1 \\subseteq I_2 \\subseteq I_3 \\subseteq \\cdots$, there exist infinitely many $n \\in \\mathbb{N}$ such that $I_n = I_{n+1}$. Does it follow that $R$ is Noetherian?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the double integral \\( \\int_F \\arctan\\left(\\frac{x}{y}\\right)\\ dx\\ dy, \\) where \\( F \\) is the region in the \\( xy \\)-plane bounded by the curves \\( x^2+y^2=1 \\), \\( x^2+y^2=4 \\), \\( y=-|x| \\), and \\( y=|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... | 510.70 MeV |
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