prompt list | ground_truth string |
|---|---|
[
{
"content": "Find the sum of the infinite series: \\[\\sum_{k=1}^\\infty\\frac{k^3+6k^2+11k+5}{(k+3)!}\\]",
"role": "user"
}
] | \dfrac{5}{3} |
[
{
"content": "Suppose we have a continuous function $f: [0,1] \\rightarrow \\mathbb{R}$ satisfying $f(x) = f(x^3)$ for all $x \\in [0,1]$. Determine the value of $f(1) - f(0)$. \\( \\boxed{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... | 2.5(1 - cos(theta)) |
[
{
"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... | 587 kpa |
[
{
"content": "Given a complex number $z$ on the unit circle, where $|z| = 1$, determine the number of connected components of the region obtained by the transformation $z \\to e^z$. Express $z$ in polar form to analyze the transformation.",
"role": "user"
}
] | 1 |
[
{
"content": "Given the process \\(Y_t = Y_{t-1} + X_t - \\phi^2 X_{t-2}\\), where \\(X_t = \\phi X_{t-1} + Z_t + Z_{t-2}\\) and \\(Z_t\\) is white noise with mean 0 and variance \\(\\sigma^2\\), identify the parameters \\((p,d,q)\\) of the ARIMA process that describes \\(Y_t\\).",
"role": "user"
}
] | (0, 1, 3) |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to \\infty} \\ \\left(\\frac{4^n-(-2)^n}{n^3}\\right)^{1/n}$$",
"role": "user"
}
] | 4 |
[
{
"content": "Is every Banach space a complete topological vector space? Consider a net $(v_\\alpha)_{\\alpha\\in I}$ in a topological vector space $(V, \\mathcal{T})$. The net is called Cauchy if for every neighborhood $U$ of $0$, there exists an index $\\alpha_0$ such that for all $\\alpha, \\beta \\geq \\alp... | Yes |
[
{
"content": "Consider the sequence \\((x_n) = \\left(\\sum_{k=1}^n \\frac{1}{k}\\right)_n\\), which is \\((1, 1+\\frac{1}{2}, 1+\\frac{1}{2}+\\frac{1}{3}, \\ldots)\\). Is it possible to find a subsequence \\((x_{r_n})\\) of \\((x_n)\\) such that \\(\\lim_{n \\to \\infty} |x_{r_{n+1}} - x_{r_n}| \\neq 0\\)?",
... | 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... | $94,347.82 |
[
{
"content": "Given that $a, b, c, d \\in [\\frac{1}{2}, 2]$ and $abcd = 1$, determine the maximum value of the expression $$(a+\\frac{1}{b})(b+\\frac{1}{c})(c+\\frac{1}{d})(d+\\frac{1}{a}).$$",
"role": "user"
}
] | 25 |
[
{
"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... | adverb clause |
[
{
"content": "When $\\frac{1}{1111}$ is expressed as a decimal, what is the sum of the first 40 digits after the decimal point?",
"role": "user"
}
] | 90 |
[
{
"content": "In a certain city, earthquake occurrences are modeled by a Poisson process with an intensity of \\( \\lambda = 2 \\) per year. The damage caused by each earthquake is exponentially distributed with a parameter \\( \\mu = 1000 \\) Euros. Calculate the expected damage per decade.",
"role": "user... | 20000 |
[
{
"content": "Find the third derivative of the function \\( f(x) = \\frac{e^x - 1}{x} \\) at \\( x = 0 \\) using the definition of the derivative, given that \\( f(0) = 1 \\).",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Find the minimum value of \\(|z_1 - z_2|\\), where \\(z_1\\) and \\(z_2\\) are the solutions of the equation \\(e^{ia}z^2 - (i + 3e^{3ia})z + 3ie^{2ia} = 0\\), with \\(a\\) being a real parameter.",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the limit of the infinite product: \\[ \\prod_{n=0}^{\\infty} \\left(1 + \\frac{1}{5^{2^n}}\\right) \\]",
"role": "user"
}
] | \dfrac{5}{4} |
[
{
"content": "Determine whether the following statement is true or false: Given a decreasing positive sequence $\\{a_n\\}$ such that $\\sum_{n=1}^{\\infty} a_n$ diverges, and a function $f: \\mathbb{N} \\rightarrow \\mathbb{N}$ with $\\lim\\limits_{n\\to\\infty} f(n) = \\infty$, if $\\sum_{n=1}^{\\infty} a_{[f(... | True |
[
{
"content": "Given that $f(0) = 0$ and $|f'(x)| \\leq |f(x)|$ for all $x > 0$, where $f$ is continuous on $[0, +∞)$ and differentiable on $(0, +∞)$, does it follow that $f(x) = 0$ for all $x \\geq 0$? Answer 'yes' or 'no' and justify your answer.",
"role": "user"
}
] | yes |
[
{
"content": "The parabola \\( P \\) has its focus a distance \\( m \\) from the directrix. The chord \\( AB \\) is normal to \\( P \\) at point \\( A \\). Determine the minimum length of the chord \\( AB \\).",
"role": "user"
}
] | 3\sqrt{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... | 34.55 m/s |
[
{
"content": "A regular hexagon with center at the origin in the complex plane has opposite pairs of sides one unit apart. One pair of sides is parallel to the imaginary axis. Let $R$ be the region outside the hexagon, and let $S = \\left\\lbrace\\frac{1}{z} \\ | \\ z \\in R\\right\\rbrace$. Find the area of $... | 3 \sqrt{3} + 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... | 317K |
[
{
"content": "Calculate the volume of the solid bounded by the surfaces \\( \\frac{x^{2}}{27}+\\frac{y^{2}}{25}=1 \\), \\( z=\\frac{y}{\\sqrt{3}} \\), and \\( z=0 \\) for \\( y \\geq 0 \\).",
"role": "user"
}
] | 50 |
[
{
"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... | u(1 + cos z)/2 |
[
{
"content": "Find the number of permutations of $n$ elements such that each element is at least $k$ positions to the right of its original position, given that $n \\geq k \\geq 1$. Provide your answer in terms of $n$ and $k$.",
"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... | Unknown |
[
{
"content": "Let \\( S = \\{(a, b, c) : a, b, c \\in \\mathbb{R} \\} \\) such that the function \\( f(z) = x + ay + i(bx + cy) \\) is analytic. Determine the isomorphism of the linear span \\( L(S) \\). Choose the correct option:\n\n(a) \\( \\mathbb{C}(\\mathbb{R}) \\)\n(b) \\( \\mathbb{R}^2(\\mathbb{R}) \\)\n... | B |
[
{
"content": "Simplify $\\frac{2m+8}{3}-\\frac{2-m}{3}$.",
"role": "user"
}
] | m+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... | 62 mph |
[
{
"content": "Determine whether the equation \\(a^2 + b^2 = 5(c^2+d^2)\\) has any integer solutions where not all of \\(a, b, c,\\) and \\(d\\) are zero.",
"role": "user"
}
] | Yes |
[
{
"content": "Given the joint probability density function (pdf) $f(x,y) = \\lambda^2 e^{-\\lambda y}$ for $0 < x < y$, where $\\lambda$ is a positive constant, find the conditional distribution of $X$ given $Y = y$. Express your answer in terms of $x$ and $y$.",
"role": "user"
}
] | \dfrac{1}{y} |
[
{
"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... | 25.47% |
[
{
"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... | 81.7% |
[
{
"content": "Let $\\mathcal{H} = l^2(\\mathbb{N})$. For $N \\geq 1$, define the linear functional $L: \\mathcal{H} \\rightarrow \\mathbb{F}$ by $L(\\{\\alpha_n\\}) = \\alpha_N$. Find the vector $h_0$ in $\\mathcal{H}$ such that $L(h) = \\langle h, h_0 \\rangle$ for every $h$ in $\\mathcal{H}$.",
"role": "u... | e_N |
[
{
"content": "Determine the greatest value of \\( \\lim_{x \\to \\infty} \\frac{f'(x)}{f(x)} \\) where \\( f(x) \\) is a solution to one of the following differential equations:\n\n1. \\( y'' + 5y' - 6 = 0, \\; y(0) = -1, \\; y'(0) = 1 \\)\n2. \\( 4y'' - 8y' + 3y = 0, \\; y(0) = 2, \\; y'(0) = 1 \\)\n3. \\( 4y'... | \dfrac{1}{2} |
[
{
"content": "Determine the group of symmetries for the elements of the quaternion group, excluding 1 and -1.",
"role": "user"
}
] | S_4 |
[
{
"content": "Find the volume of the region in \\( \\mathbb{R}^3 \\) bounded by the surfaces \\( y = x^2 \\), \\( x = y^2 \\), \\( z = 0 \\), and \\( z = xy \\).",
"role": "user"
}
] | \dfrac{1}{12} |
[
{
"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... | 20 kcal |
[
{
"content": "Let $a, b, c$ be the roots of the polynomial $x^3 - 9x^2 + 11x - 1 = 0$. Define $s = \\sqrt{a} + \\sqrt{b} + \\sqrt{c}$. Calculate the value of $s^4 - 18s^2 - 8s$. \\[ \\boxed{} \\]",
"role": "user"
}
] | -37 |
[
{
"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... | 0.018 L or 18 mL |
[
{
"content": "Determine whether it is possible to inscribe a rectangle in an ellipse such that the sides of the rectangle are not parallel to the major or minor axes of the ellipse. Answer with 'Yes' or 'No'.",
"role": "user"
}
] | No |
[
{
"content": "Consider the exact sequence of abelian groups:\n\n$$0 \\to \\mathbb{Z}^k \\to \\mathbb{Z}^m \\to \\mathbb{Z}^n \\to 0.$$ After tensoring this sequence with $\\mathbb{Q}$, determine the relationship between $k$, $m$, and $n$.",
"role": "user"
}
] | m = k + 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... | 6.72 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... | 256764.91 |
[
{
"content": "The lines $y = -2x + 8$ and $y = \\frac{1}{2} x - 2$ meet at $(4,0),$ as shown. What is the area of the triangle formed by these two lines and the line $x = -2?$ [asy]\ndraw((-8,0)--(15,0),black+linewidth(1));\ndraw((-8,0)--(15,0),EndArrow);\ndraw((0,-8)--(0,15),black+linewidth(1));\ndraw((0,-8)--... | 45 |
[
{
"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... | Sales (16000, 18000, 20000 units): $3,424,000, $3,852,000, $4,280,000
Direct materials (16000, 18000, 20000 units): $392,000, $441,000, $490,000
Direct labor (16000, 18000, 20000 units): $676,000, $760,500, $845,000
Production supplies (16000, 18000, 20000 units): $432,640, $486,720, $540,800
Sales commission (16000, 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... | The decrease in consumer income leads to a decrease in demand, shifting the demand curve to the left. The increase in the cost of providing tertiary education leads to a decrease in supply, shifting the supply curve to the left. The combined effect is a definite decrease in equilibrium quantity. The effect on equilibr... |
[
{
"content": "Given triangle $ABC,$ there exists a unique point $P$ such that\n\\[AB^2 + AP^2 + BP^2 = AC^2 + AP^2 + CP^2 = BC^2 + BP^2 + CP^2.\\]Express the common value above in terms of the side lengths $a,$ $b,$ and $c,$ and circumradius $R$ of triangle $ABC.$",
"role": "user"
}
] | 32R^2 - 3(a^2 + b^2 + c^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... | 22.9 ft/s |
[
{
"content": "Let $A$ be a finite abelian group of order $360$ which does not contain any elements of order $12$ or $18$. How many elements of order $6$ does $A$ contain?",
"role": "user"
}
] | 56 |
[
{
"content": "Find the maximum value of the function \\( f(t) = 16\\cos t \\cdot \\cos 2t \\cdot \\cos 3t \\cdot \\cos 6t \\).",
"role": "user"
}
] | 16 |
[
{
"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... | 0.0674 M |
[
{
"content": "Simplify the expression \\((\\sqrt{10}+\\sqrt{11}+\\sqrt{12})(\\sqrt{10}+\\sqrt{11}-\\sqrt{12})(\\sqrt{10}-\\sqrt{11}+\\sqrt{12})(-\\sqrt{10}+\\sqrt{11}+\\sqrt{12})\\) without directly multiplying everything out.",
"role": "user"
}
] | 359 |
[
{
"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... | 0.132 m/s |
[
{
"content": "Consider a set of 2011 natural numbers. All their 2011\\(\\cdot\\)1005 pairwise sums are written on the board. Is it possible that exactly one-third of these sums are divisible by 3, and another one-third give a remainder of 1 when divided by 3?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the set \\(\\{ (x,y) \\in \\mathbb{R}^2 \\mid x^3 + y^3 = 1 \\}\\) is a manifold in \\(\\mathbb{R}^2\\).",
"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... | 47.2 degrees |
[
{
"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 m/s^2 |
[
{
"content": "Compare the smallest positive roots of the equations \\( \\cos(\\sin x) = x \\) and \\( \\sin(\\cos x) = x \\) within the interval \\([0, \\frac{\\pi}{2}]\\). Let \\(x_1\\) be the root of \\(\\sin(\\cos x) = x\\) and \\(x_2\\) be the root of \\(\\cos(\\sin x) = x\\). Determine which is greater: \\... | x_2 |
[
{
"content": "Six points are equally spaced around a circle of radius 1. Three of these points are the vertices of a triangle that is neither equilateral nor isosceles. What is the area of this triangle?",
"role": "user"
}
] | \frac{\sqrt3}{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... | 1.7 g |
[
{
"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... | 3.39kgm^2s^(-1) |
[
{
"content": "In space, there are \\( n \\) (\\( n \\geqslant 3 \\)) planes, where any three planes do not share a common perpendicular plane. Consider the following four assertions:\n\n1. No two planes are parallel to each other.\n2. No three planes intersect in a single line.\n3. Any two intersection lines be... | 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... | 7 seconds |
[
{
"content": "Given the ellipse \\(\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1\\) where \\(a>b>0\\), let \\(A\\) be the left vertex and \\(F(c, 0)\\) be the right focus. Suppose \\(2b\\), \\(a\\), and \\(c\\) form a geometric progression. A line through \\(F\\) intersects the ellipse at points \\(M\\) and \\(N\... | 90^\circ |
[
{
"content": "Determine the number of vectors in the three-dimensional vector space over the finite field $\\Bbb F_3$ that are fixed under the action of the permutation group $S_3$, where the action is defined by $\\sigma\\cdot e_i = e_{\\sigma(i)}$ for all $\\sigma \\in S_3$ and $i=1,2,3$. What is the cardinal... | 3 |
[
{
"content": "Determine the value of the Ramsey number $R(K_3, C_5)$. Use the hint that $R(3,4) = 9$ to assist in your calculation.",
"role": "user"
}
] | 9 |
[
{
"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... | 5.52% |
[
{
"content": "Evaluate the limit as $n$ approaches infinity of the integral: $$\\int_0^\\infty \\frac{\\cos(nx)}{1+x^n}\\,dx$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following statement is true or false: If \\(\\lim\\limits_{n\\to \\infty} \\frac{1}{n}\\sum\\limits_{i=1}^n a_i = L\\), where \\(\\{a_n\\}\\) is a real sequence, then \\(\\lim\\limits_{n\\to \\infty} \\left|a_n - L \\right|= 0\\).",
"role": "user"
}
] | B |
[
{
"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... | 1.44% |
[
{
"content": "Determine whether the non-degeneracy of the Hessian matrix at a critical point implies that the critical point is isolated, even if the function is not positive or negative definite.",
"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... | $44,000 |
[
{
"content": "Find all values of $a$ such that the equation $\\cos(ax) = a \\cdot \\cos(x)$ holds true for every $x \\in \\mathbb{R}$. It is given that $a = 1$ is a solution. Are there any other values of $a$ that satisfy the equation?",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the area enclosed by the curve \\(a^2x^2 = y^3(2a-y)\\) using a double integral. The curve is symmetric about the \\(y\\)-axis and intersects the \\(y\\)-axis at \\(y=0\\) and \\(y=2a\\). Set up and evaluate the double integral to find the total area.",
"role": "user"
}
] | \pi a^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... | \int_{\alpha}^{\beta} \frac{1}{2} \sqrt{\frac{l}{g}} \frac{d \theta}{\sqrt{\sin^2 (\alpha /2) - \sin^2 (\theta /2)}} = \sqrt{\frac{l}{g}} \int_{\pi /2}^{\Phi} \frac{d \phi }{\sqrt{1 - k^2 \sin^2 \phi}} |
[
{
"content": "Find the radius of convergence of the complex power series $$\\sum_{n=2}^\\infty \\frac{1}{n!}(z-2n\\pi i)^{n-2}.$$",
"role": "user"
}
] | 0 |
[
{
"content": "An infinite sequence of positive integers $a_1, a_2, \\ldots$ is defined such that for $k \\geq 2$, the $k^\\text{th}$ element $a_k$ is equal to $k$ plus the product of the first $k-1$ elements of the sequence. Given that $a_1 = 1$, determine the smallest prime number that does not divide $a_{2010... | 5 |
[
{
"content": "In an acute triangle $\\triangle ABC$, the altitudes $AD, BE, CF$ intersect at the orthocenter $H$. Given the side lengths $BC = a$, $AC = b$, and $AB = c$, determine the value of $A H \\cdot A D + B H \\cdot B E + C H \\cdot C F$.\n\n(A) $\\frac{1}{2}(ab + bc + ca)$ \n(B) $\\frac{1}{2}\\left(a^{... | B |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\left(1 - \\frac{(1+\\frac{2}{n})^n}{n}\\right)^n \\]",
"role": "user"
}
] | e^{-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... | 2.1e12 |
[
{
"content": "Find the minimum value of \\( f(a,b,c) = \\int_0^1 (a+bx+cx^2)^2 \\, dx \\) subject to the constraint \\( a+b+c=1 \\).",
"role": "user"
}
] | \dfrac{1}{9} |
[
{
"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... | 10.1% |
[
{
"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... | 32900 |
[
{
"content": "In a game involving a $2016\\times2016$ empty matrix, Alice and Bob take turns filling the matrix with real numbers, with Alice going first. If the determinant of the final matrix is non-zero, Alice wins; otherwise, Bob wins. Determine who has the winning strategy.",
"role": "user"
}
] | Bob |
[
{
"content": "Determine whether the inequality \\( P(X+Y>\\delta)\\leq P(X>\\delta/2)+P(Y>\\delta/2) \\) holds universally for any positive random variables \\( X \\) and \\( Y \\) and any \\( \\delta>0 \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the definite integral: \\[ \\int_{-1}^{3} \\left( \\tan^{-1}\\left(\\frac{x}{x^2+1}\\right) + \\tan^{-1}\\left(\\frac{x^2+1}{x}\\right) \\right) \\, dx \\]",
"role": "user"
}
] | \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... | 7380 m/s |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to \\infty} \\frac{1}{n^3}\\sum_{k=1}^n \\frac{k^2}{a_k} \\] where \\( a_n \\) is a sequence of real numbers defined by \\( a_1=1 \\) and \\( a_{n+1}=\\dfrac{a_n}{1+na_n} \\).",
"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... | 0.05463 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... | 0.31 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... | 35.73% |
[
{
"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... | $10,360 |
[
{
"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... | 0.72 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... | $(x_0+v_{x_0}t)^2+(y_0+v_{y_0}t)^2 = c^2t^2$ |
[
{
"content": "Find the limiting value of the Beta function \\( B(a,b) = \\int_0^1 x^{a -1}(1-x)^{b-1}\\,d x \\) as \\(a \\to \\infty\\), \\(b \\to \\infty\\), and \\(a,b \\to \\infty\\).",
"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... | $614,420.67 |
[
{
"content": "Is it possible to define an operator norm on \\(\\mathbb{C}^d\\) such that every element of a given bounded semigroup of complex \\(d \\times d\\) matrices has a norm less than or equal to 1?",
"role": "user"
}
] | Yes |
[
{
"content": "The sum of a whole number and the next four consecutive whole numbers is $105$. Find the result when the mean of the numbers is subtracted from the median of the numbers.",
"role": "user"
}
] | 0 |
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