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... | $1,016,698.58 |
[
{
"content": "Determine whether the following statement is true or false:\n\nIf $U$ is any domain, $f$ is any function continuous on $U$, and $\\gamma$ is any closed contour such that its image and its interior lie in $U$, then \\( \\int_\\gamma f(z)\\,dz = 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... | 94300 |
[
{
"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... | (2/3)ML^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 cm |
[
{
"content": "Evaluate the integral \\( I = \\int_0^\\infty \\frac{1}{x^2 + b^2} \\, dx \\) using complex analysis methods, where \\( b > 0 \\).",
"role": "user"
}
] | \dfrac{\pi}{2b} |
[
{
"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... | 21,612.9 lb-ft |
[
{
"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... | 8.89 m |
[
{
"content": "Let \\( f(x) = e^{x^2} \\) be a function defined on \\( \\mathbb{R} \\). Let \\( F \\) be an antiderivative of \\( f \\). Calculate the limit: \\[ \\lim_{x \\rightarrow \\infty} \\frac{xF(x)}{f(x)}. \\]",
"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... | 1.5L |
[
{
"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 mol L^(-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... | 8.97e-6 1/(M-s) |
[
{
"content": "Find the value of \\( \\lambda \\) that minimizes the integral \\( \\int_{0}^{\\pi}\\sin^2(x-\\lambda x) \\, dx \\).",
"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... | $47,221.08 |
[
{
"content": "Let $S = \\{m + \\frac{1}{n} \\mid m, n \\in \\mathbb{N}\\}$. Determine the derived set (the set of cluster points) of $S$. \\( \\mathbb{N} \\) denotes the set of natural numbers.",
"role": "user"
}
] | \mathbb{N} |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\left( \\sqrt[n]{n^2} + \\frac{2}{n} \\right)^{\\frac{n}{\\ln n}}$$",
"role": "user"
}
] | e^2 |
[
{
"content": "For $a > 0$ and $0 < x_0 < \\frac{2}{a}$, let the sequence $(x_n)_{n \\in \\mathbb{N}_0}$ be defined by the recurrence relation $x_{n+1} = x_n(2 - ax_n)$. Show that the sequence $(x_n)$ converges and determine its limit.",
"role": "user"
}
] | \dfrac{1}{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... | 0.245 T, East |
[
{
"content": "What is the remainder when 1,234,567,890 is divided by 99?",
"role": "user"
}
] | 72 |
[
{
"content": "Consider the sequence \\( a_n = \\frac{1000^n}{n!} \\) for \\( n \\in \\mathbb{N} \\). Determine the value of \\( n \\) for which \\( a_n \\) is greatest. Choose the correct answer from the following options: (A) \\( n=998 \\) (B) \\( n=999 \\) (C) \\( n=1000 \\) (D) \\( n=1001 \\).",
"role": ... | C |
[
{
"content": "Given that the aggregate claims \\(\\sum_{X=i}^N X_{i}\\) follow a compound Poisson distribution with individual claim distribution probabilities \\(P(X=1) = \\frac{1}{3}\\) and \\(P(X=3) = \\frac{2}{3}\\), and the condition \\(P(S=4)=P(S=3)+6P(S=1)\\), find the expectation of the claim count \\(N... | 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... | 0.745 |
[
{
"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... | $1254 |
[
{
"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... | -18.75 Newtons |
[
{
"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... | $21,560.02 |
[
{
"content": "What is the probability that an event with probability \"p\" occurs exactly twice in an infinite sequence of independent trials?",
"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... | 8.74 min |
[
{
"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... | 120 |
[
{
"content": "Evaluate the integral: $$\\int_{0}^{\\pi }\\frac{\\sin 2017x}{\\sin x}\\mathrm{d}x$$",
"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... | $7919.17 |
[
{
"content": "Evaluate the integral \\( \\iint_D \\sin(x^2+y^2)~dA \\) by transforming it to polar coordinates, where \\( D \\) is the region in the first quadrant bounded by the lines \\( x=0 \\) and \\( y=\\sqrt{3}x \\) and the circles \\( x^2+y^2=2\\pi \\) and \\( x^2+y^2=3\\pi \\).",
"role": "user"
}
... | \dfrac{\pi}{6} |
[
{
"content": "Evaluate the integral \\( \\int_{\\lvert z\\rvert=1}(z-1)^2\\lvert dz\\rvert \\).",
"role": "user"
}
] | 2\pi |
[
{
"content": "Evaluate the limit of the sequence: \\[ \\lim_{n\\to\\infty} \\frac{e^{\\ln n \\ln \\ln \\ln n}}{\\sqrt{2\\pi \\ln n} (\\ln n)^{\\ln n}}. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Is the isometry group of a simply-connected Ricci-flat closed manifold finite?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the number of ways to express 527 as a sum of three squares.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: $$\\lim_{(x,y,z)\\to (0,0,0)}\\frac{1}{x^2+y^2+z^2}e^{-\\frac{1}{\\sqrt{x^2+y^2+z^2}}}$$",
"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... | Glycogen |
[
{
"content": "Let \\( f(x) \\) be a function defined on \\( \\mathbf{R} \\). Given that \\( f(0) = 2008 \\) and for any \\( x \\in \\mathbf{R} \\), the conditions \\( f(x+2) - f(x) \\leq 3 \\cdot 2^x \\) and \\( f(x+6) - f(x) \\geq 63 \\cdot 2^x \\) hold, find \\( f(2008) \\).",
"role": "user"
}
] | 2^{2008} + 2007 |
[
{
"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... | 2.9e2 K |
[
{
"content": "If the real numbers \\(\\alpha, \\beta, \\gamma\\) form a geometric sequence with a common ratio of 2, and \\(\\sin \\alpha, \\sin \\beta, \\sin \\gamma\\) form a geometric sequence, find the value of \\(\\cos \\alpha\\).",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{1} f(x)f'(x) (1+2(f'(x))^2+2f(x)f''(x)) \\, dx \\) given that \\( f(x) \\) has a continuous second derivative on \\([0,1]\\) and satisfies \\( f(0)=0 \\), \\( f'(0)=0 \\), \\( f(1)=1 \\), and \\( f'(1)=3 \\).",
"role": "user"
}
] | \dfrac{19}{2} |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{+\\infty} x \\cdot \\frac{1}{2}e^{-|x|} \\, dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the convergence of the series \\( \\sum\\limits_{n=1}^{\\infty} \\frac{2n+1}{3n^2+1} x^n \\) in terms of \\( x \\).",
"role": "user"
}
] | [-1, 1) |
[
{
"content": "Let $X$ be a Banach space and $\\{ f_n \\}_{n \\ge 1} \\in X'$. If there exists $C \\ge 0$ such that for each $F \\in X''$, \\( \\sum_{n = 1}^\\infty | F(f_n) | \\le C \\left\\Vert F \\right\\Vert \\), does it follow that \\( \\sum_{n = 1}^\\infty | f_n(x) | < \\infty \\) for all $x \\in X$? Answe... | Yes |
[
{
"content": "If $y = -x^2 + 5$ and $x$ is a real number, then what is the maximum value possible for $y$?",
"role": "user"
}
] | 5 |
[
{
"content": "Consider the function \\( p(z,w) = a_0(z) + a_1(z) w + \\dots + a_k(z) w^k \\), where \\( k \\ge 1 \\) and \\( a_i(z) \\) are non-constant polynomials of \\( z \\). Determine the correct property for the set \\( A = \\{(z,w) \\in \\mathbb{C}^2 : p(z,w) = 0\\} \\):\n\nA. Bounded with empty interior... | B |
[
{
"content": "Determine whether there exists an infinite monoid $H$, generated by a finite set of generators $\\{h_1, \\ldots, h_n\\}$ with $n > 1$, that is not a free monoid and does not contain any free monoid as a submonoid.",
"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... | 198 grams |
[
{
"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... | $1,185,720 |
[
{
"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... | 1.2139 |
[
{
"content": "Evaluate the sum \\( \\sum_{\\textbf{t} \\in \\mathbb{Z}_{3}^{d}} \\omega^{\\textbf{t}\\cdot(\\textbf{p} + \\textbf{q})} \\) where \\( \\textbf{p} \\neq \\textbf{q} \\in \\mathbb{Z}_{3}^{d} \\) and \\( \\omega = e^{2\\pi i/3} \\) is a primitive cube root of unity.",
"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... | $933.86 |
[
{
"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... | Treasury bills, commercial paper, or certificates of deposit |
[
{
"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... | $28,500 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\frac{1 - \\frac{x^2}{2} - \\cos \\left(\\frac{x}{1-x^2}\\right)}{x^4} \\] using the fact that \\( \\lim_{x \\to 0} \\frac{1-\\cos x}{x^2}=\\frac{1}{2} \\).",
"role": "user"
}
] | \dfrac{23}{24} |
[
{
"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... | 114.71 kg |
[
{
"content": "Determine whether a pointwise limit of continuous functions can be discontinuous on a non-dense subset of the domain. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find all real positive solutions for the system of equations:\n\\[x + y^2 + z^3 = 3\\]\n\\[y + z^2 + x^3 = 3\\]\n\\[z + x^2 + y^3 = 3\\]",
"role": "user"
}
] | (1, 1, 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... | 4.45 |
[
{
"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... | {eq}I=\frac{3mr^2}{5}{/eq} |
[
{
"content": "Let $g:\\mathbb{R}\\to\\mathbb{R}$ be a differentiable function such that $\\lim\\limits_{x\\to\\pm\\infty}x^2g(x)=0$. Given that $\\int_{-\\infty}^{+\\infty} g^2(x)dx=2$, find the value of $\\int_{-\\infty}^{+\\infty} xg(x)g'(x)dx$. \\(\\boxed{\\text{Your answer here}}\\)",
"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... | -1.22e-15 J |
[
{
"content": "A trapezoid has one angle measuring $60^{\\circ}$. If a circle can be both inscribed in and circumscribed around the trapezoid, find the ratio of its bases.",
"role": "user"
}
] | 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... | 3443 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... | 2H_2S + 3O_2 -> 2SO_2 + 2H_2O |
[
{
"content": "Evaluate the contour integral \\(\\oint_{C}\\frac{e^z+\\sin z}{z^5}dz,\\) where \\(C\\) is the path defined by \\(r(t) = 3 + e^{2\\pi i t}\\) for \\(t \\in [0,1]\\), using Cauchy's integration formula.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the definite integral: $$\\int_0^1((1-x)^8x^{11}-(1-x)^{11}x^8)dx$$.",
"role": "user"
}
] | 0 |
[
{
"content": "Find the derivative of the inverse function of \\( f(x) = x^2 + x + e^x \\) at \\( x=1 \\), if it exists.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Let $H$ be a finite subgroup of a group $G$. Is the number of left cosets of $H$ in $G$ always finite?",
"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... | 8.60 ml |
[
{
"content": "Darren has borrowed $100$ clams from Ethan at a $10\\%$ simple daily interest. Meanwhile, Fergie has borrowed $150$ clams from Gertie at a $5\\%$ simple daily interest. In how many days will Darren and Fergie owe the same amounts, assuming that they will not make any repayments in that time period... | 20\text{ days} |
[
{
"content": "A regular $4n$-gon $A_{1} A_{2} \\ldots A_{4n}$ has an area of $S$, where $n > 1$. Determine the area of the quadrilateral $A_{1} A_{n} A_{n+1} A_{n+2}$.",
"role": "user"
}
] | \dfrac{S}{2n} |
[
{
"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-bromo-4-hexene |
[
{
"content": "Determine whether the derivative of a decreasing and bounded $C^1$ function on $\\mathbb{R}$ necessarily converges to 0.",
"role": "user"
}
] | No |
[
{
"content": "Find all positive integers \\( n \\) such that \\( \\left(\\frac{-1 + i\\sqrt{3}}{2}\\right)^n + \\left(\\frac{-1 - i\\sqrt{3}}{2}\\right)^n = 2. \\)",
"role": "user"
}
] | 3k |
[
{
"content": "Find the value of \\( p > 1 \\) such that the series \\( \\sum_{n=1}^{\\infty} f_n \\) converges in \\( L^p(\\mathbb{R}) \\), where:\n\\[\nf_n(x) = \\frac{1}{1+n^2\\sqrt{x}}\\chi_{[\\exp(2n),2\\exp(2n+2)]}(x)\n\\]",
"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... | 10^14 |
[
{
"content": "Determine the smallest positive integer $n$ such that in any two-coloring of a complete graph $K_n$, there exist $m$ pairwise disjoint edges of the same color.",
"role": "user"
}
] | 3m - 1 |
[
{
"content": "The first four terms in an arithmetic sequence are $x+y$, $x-y$, $xy$, and $x/y$, in that order. What is the fifth term? Express your answer as a common fraction.",
"role": "user"
}
] | \frac{123}{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... | pH - \log[OH-] = 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... | 1.1e-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... | K(1/2-1/sqrt(30)) |
[
{
"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... | 3.54% |
[
{
"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... | 1.73 |
[
{
"content": "Calculate \\(42^{17} \\pmod{3233}\\) without using a calculator or modular exponentiation techniques.",
"role": "user"
}
] | 2557 |
[
{
"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... | 1.37 m |
[
{
"content": "At a certain moment, the instantaneous power of the wind acting on a sailboat reaches its maximum value. Given the formula for the force of the airflow on the sail \\( F=\\frac{C S \\rho\\left(v_{0}-v\\right)^{2}}{2} \\), where \\( C \\) is the aerodynamic force coefficient, \\( S \\) is the sail ... | \dfrac{v_0}{3} |
[
{
"content": "Let $K$ be the field with exactly $7$ elements. Let $\\mathscr{M}$ be the set of all $2 \\times 2$ matrices with entries in $K$. How many elements of $\\mathscr{M}$ are similar to the matrix \\( \\begin{pmatrix} 0 & 0 \\\\ 0 & 1 \\end{pmatrix} \\)?",
"role": "user"
}
] | 56 |
[
{
"content": "Find the minimum value of the trace of the matrix product $AA^T$ for an $n \\times n$ non-singular matrix $A$ with integer entries.",
"role": "user"
}
] | n |
[
{
"content": "Find \\( \\lim_{n\\rightarrow \\infty} \\frac{\\sqrt{1}+\\sqrt{2}+\\sqrt{3}+\\cdots+\\sqrt{n}}{n^{3/2}} \\).",
"role": "user"
}
] | \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... | 79.1 mL |
[
{
"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... | 149750 |
[
{
"content": "Compute the integral \\( \\int_{M=L(3;1,1,1)} X p_1(M) \\), where \\( M = S^5/\\mathbb{Z}_3 \\) is a Lens space, \\( X \\in H^1(M, \\mathbb{Z}_3) \\), and \\( p_1(M) \\) is the first Pontryagin class of \\( M \\). What is the value of this integral?",
"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... | The criteria include:
1. In-house costs (fixed costs of manufacturing overhead and variable costs of labor and materials).
2. Whether the plant has excess capacity in space or labor.
3. The potential effect of overtime labor costs.
4. The benefit of better control of quality and delivery times when making the item in-house.
5. The potential cost of losing volume or shipping discounts from current suppliers. |
[
{
"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... | $148,529.05 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{2\\pi}\\log(\\sin(2t))dt \\) using the method of symmetry and the fact that \\( \\int_{0}^{\\pi}\\log(\\sin(t))dt=-\\pi\\log(2) \\).",
"role": "user"
}
] | -2\pi \log 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... | $4,680,993 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{100}\\left\\{ \\sqrt{x}\\right\\} \\,dx \\) where \\( \\{.\\} \\) denotes the fractional part of \\( x \\).",
"role": "user"
}
] | \dfrac{155}{3} |
[
{
"content": "Let $R$ be a ring with finitely many maximal ideals such that $R_{\\mathfrak m}$ is a noetherian ring for each maximal ideal $\\mathfrak m$. Is $R$ necessarily a noetherian ring?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $\\lbrace N(t)\\rbrace_{t\\geq 0}$ be a Poisson process with intensity $\\lambda = 3$. Compute the probability $P\\left[N(6) = 2 \\,|\\, N(8) = 4, N(3) = 1\\right].$",
"role": "user"
}
] | \dfrac{36}{125} |
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