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... | 26.2Nm |
[
{
"content": "Determine whether it is possible to find matrices \\(X\\), \\(Y\\), and \\(Z\\) such that \\(X = Z^{-1} Y Z\\) but \\(X \\neq Y\\), given that \\(Z\\) is invertible.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the range of values of \\( b \\) for which the solution \\( u(t) \\) of the initial value problem \\( u'(t) = Bu(t), \\; t > 0 \\) and \\( u(0) = u_0 \\), where \\( u_0 \\) is a given vector in \\( \\mathbb{R}^2 \\) and \\( B = \\begin{bmatrix} -1 & 2 \\\\ -1 & b \\end{bmatrix} \\), sati... | (-\infty, 1) |
[
{
"content": "Let $X$ be a projective scheme and $Y \\subset X$ be a projective subscheme, with both $X$ and $Y$ being connected. Denote by $i:Y \\hookrightarrow X$ the closed immersion. Is the induced morphism $H^0(\\mathcal{O}_X) \\to H^0(i_*\\mathcal{O}_Y)$ always surjective?",
"role": "user"
}
] | No |
[
{
"content": "Find the number of Sylow 5-subgroups in the alternating group $A_5$.",
"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... | 1.16e-4 eV |
[
{
"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... | 0.322 mole/L |
[
{
"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... | 26.25 mi |
[
{
"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... | Sodium hydroxide, NaOH |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to \\infty}\\frac{e^n}{(n/e)^n\\sqrt{n}}$$",
"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... | 15.45 g |
[
{
"content": "Evaluate the integral: \\[ \\int_0^2 \\left((1+x^3)^{1/2} + (x^2+2x)^{1/3}\\right) \\, dx \\]",
"role": "user"
}
] | 6 |
[
{
"content": "Determine the value of $k$ such that the equation $(1+x^2)e^x-k=0$ has exactly one real root.",
"role": "user"
}
] | \dfrac{2}{e} |
[
{
"content": "Sean adds up all the even integers from 2 to 500, inclusive. Julie adds up all the integers from 1 to 250, inclusive. What is Sean's sum divided by Julie's sum?",
"role": "user"
}
] | 2 |
[
{
"content": "Find the coefficient of \\(x^{15}\\) in the expansion of \\((1-x^2)^{-10}(1-2x^9)^{-1}\\).",
"role": "user"
}
] | 440 |
[
{
"content": "Let \\( F \\) be a subset of \\( \\mathbb{R}^n \\) with finite Lebesgue measure. If \\( F \\) is dense in \\( \\mathbb{R}^n \\), does it follow that the Lebesgue measure of the boundary of \\( F \\) is infinite? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Solve for $a$: $$\\sqrt{4+\\sqrt{16+16a}}+ \\sqrt{1+\\sqrt{1+a}} = 6.$$",
"role": "user"
}
] | 8 |
[
{
"content": "Find the minimum value of the expression \\( \\sqrt{\\sin^{4} A + 1} + \\sqrt{\\cos^{4} A + 4} \\) where \\( \\angle A \\) is an acute angle.",
"role": "user"
}
] | \sqrt{10} |
[
{
"content": "Evaluate the integral \\( \\frac{1}{2\\pi} \\int_{0}^{2\\pi} e^{\\cos\\theta} \\cos(n\\theta) \\,d\\theta \\) using the residue theorem.",
"role": "user"
}
] | I_n(1) |
[
{
"content": "Does there exist an uncountable set $S$ of sets such that it is closed under finite union and uncountable union, but not always closed under countably infinite union?",
"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... | $14.60 |
[
{
"content": "Determine the maximum number of perfect matchings in a genus $g$ balanced bipartite graph, where the number of vertices for each color is within a difference of 1. Specifically, is the maximum number of perfect matchings $2^{O(n\\log g)}$ for $k=2$?",
"role": "user"
}
] | 2^{O(n \log g)} |
[
{
"content": "Consider the functional equation \\( f(x + y) = f(x)f(y) \\). Given that \\( f'(0) = 4 \\) and \\( f(3) = 8 \\), find \\( f'(3) \\).",
"role": "user"
}
] | 32 |
[
{
"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... | 1.24e-7 |
[
{
"content": "Find the last two digits of the number $9^{9^9}$.",
"role": "user"
}
] | 89 |
[
{
"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... | 6,804 units |
[
{
"content": "Evaluate the infinite series \\(\\sum_{n=2}^{\\infty} \\frac{2n+5}{n^3+4n^2+3n}\\) using partial fraction decomposition and find its value.",
"role": "user"
}
] | \dfrac{67}{72} |
[
{
"content": "Let $f: \\mathbb{R}^n \\to \\mathbb{R}^n$ be a continuous function such that $\\int_{\\mathbb{R}^n} |f(x)| \\, dx < \\infty$. Let $A$ be a real $n \\times n$ invertible matrix and for $x, y \\in \\mathbb{R}^n$, let $\\langle x, y \\rangle$ denote the standard inner product in $\\mathbb{R}^n$. Dete... | 1 |
[
{
"content": "Determine whether the eigenvalues of a specific type of tridiagonal matrix are always positive.",
"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... | $1,120,925.09 |
[
{
"content": "Three nonzero real numbers are given. If they are used in any order as coefficients of a quadratic trinomial, and each of these trinomials has a real root, does it necessarily follow that each of these trinomials also has a positive root? Answer 'yes' or 'no' and justify your answer.",
"role":... | yes |
[
{
"content": "Find the constant $c \\neq 0$ such that the integral $\\int_{-1}^\\infty{\\frac{e^{\\frac{x}{c}}}{\\sqrt{|x|}(x+2)}dx}$ is convergent.",
"role": "user"
}
] | c < 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... | $16,449.27 |
[
{
"content": "Determine whether the limit \\( \\lim_{n\\rightarrow\\infty} \\frac{P(n)}{A(n)} \\) exists, where \\( P(n) \\) is the number of perfect numbers less than or equal to \\( n \\), and \\( A(n) \\) is the number of amicable numbers less than \\( n \\). If the limit exists, find its value.",
"role"... | 0 |
[
{
"content": "Determine the radius of convergence for the series \\(\\sum_{k=0}^{\\infty} \\frac{-(1)^k (4^k -3)x^{2k}}{k^4+3}\\) using the ratio test.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Evaluate the contour integral \\( \\oint_{|z|=3} \\frac{1}{\\sin^2 z} \\, dz \\).",
"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... | 34140 |
[
{
"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... | $4,897.06 |
[
{
"content": "Evaluate the definite integral \\( \\alpha = \\int_{\\pi/6}^{\\pi/3} \\frac{\\sin t + \\cos t}{\\sqrt{\\sin 2t}} \\, dt \\). Then, find the value of \\( f(\\alpha) = (2\\sin(\\alpha/2) + 1)^2 \\).",
"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... | 6167.06 |
[
{
"content": "Find the radius of convergence of the power series \\( \\sum a_{n}x^{n} \\), where \\( a_{0}=0 \\) and \\( a_{n}=\\frac{\\sin(n!)}{n!} \\) for \\( n\\geq 1 \\).",
"role": "user"
}
] | \infty |
[
{
"content": "Determine whether there exists a natural number that can be expressed as the product of two palindromes in more than 100 different ways. A palindrome is a natural number that reads the same forwards and backwards.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the natural number $k$ such that the equation $x^3 + y^3 + z^3 = kx^2y^2z^2$ has positive integer solutions for $x$, $y$, and $z$.",
"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... | 1737 L |
[
{
"content": "Let $(X, \\mathcal{X})$ and $(Y,\\mathcal{Y})$ be measurable spaces, and $f: X \\to Y$ a measurable function. Let $A \\in \\mathcal{X}$ be a measurable subset of $X$. Is the restricted function $f_{\\mid A}: A \\to Y$ measurable with respect to the $\\,\\sigma$-algebra $\\mathcal{A}=\\{ S \\cap A ... | Yes |
[
{
"content": "Provide an example of a sequence of functions that is monotone, bounded, but not uniformly convergent.",
"role": "user"
}
] | f_n(x) = x^n |
[
{
"content": "Given two probability measures \\(\\mu\\) and \\(\\mu'\\) over the sigma algebra \\(\\Sigma\\) of Lebesgue measurable subsets of \\([0,1]\\), both assigning measure 0 to all and only null sets, consider the collection of functions:\n\\[\\{f_X:X\\rightarrow \\overline{X} \\mid X\\in \\Sigma, 0<\\la... | \mu = \mu' |
[
{
"content": "Determine which of the following substitutions can transform the differential equation \\(y' = \\frac{y}{x^2} + x^3y^3\\) into a first-order linear equation in terms of \\(v(x)\\):\n\n1. \\(v(x) = x^3y^3\\)\n2. \\(v(x) = y^2\\)\n3. \\(v(x) = y^{-2}\\)\n4. \\(v(x) = \\frac{y}{x}\\)\n\nProvide the c... | 3 |
[
{
"content": "Determine the number of ways to arrange 6 pairs of plants in a row such that no two plants from the same pair are adjacent.",
"role": "user"
}
] | 168422400 |
[
{
"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 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... | Super Pool Service, Inc Trial balance June 30, 2012 Account Debit Credit Cash $5,200 Accounts receivable $10,600 Land $28,800 Accounts payable $4,400 Note payable $9,500 Common stock $5,100 Retained earnings $25,600 Dividends $6,100 Service revenue $17,100 Utilities expense $2,100 Delivery expense $700 Salar... |
[
{
"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... | 5250 kJ/mol |
[
{
"content": "Let\n\\[f(x) = x^3 + 6x^2 + 16x + 28.\\]The graphs of $y = f(x)$ and $y = f^{-1}(x)$ intersect at exactly one point $(a,b).$ Enter the ordered pair $(a,b).$",
"role": "user"
}
] | (-4,-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... | 66.77 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... | m/s^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... | $888.11 |
[
{
"content": "Determine the number of solutions to the equation \\( \\sin^{-1}[x^2+\\frac{1}{3}]+\\cos^{-1}[x^2-\\frac{2}{3}]=x^2 \\) for \\( x \\in [-1,1] \\), where \\([x]\\) denotes the greatest integer less than or equal to \\(x\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find the number of solutions to the equation \\(x_1 + x_2 + x_3 + \\ldots + x_6 = 20\\) where each \\(x_i\\) is an integer satisfying \\(0 \\le x_i \\le 8\\).",
"role": "user"
}
] | 27237 |
[
{
"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... | 460.44 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... | 0.278 M |
[
{
"content": "Determine the constant \\( c \\) such that:\n\\[ \\int_{0}^{x} f(t) \\, dt = \\int_{x}^{1} t^2 f(t) \\, dt + \\frac{x^8}{8} + \\frac{x^6}{6} - \\frac{c}{24} \\]\nwhere \\( f: [0,1] \\to \\mathbb{R} \\) is a continuous function.",
"role": "user"
}
] | 3 |
[
{
"content": "Given a real analytic function $f: \\mathbb R \\to \\mathbb R$ in a neighborhood of the origin, with its power series representation $$f(x) = \\sum_{k=0}^\\infty \\frac{f^{(k)}(0)}{k!} x^k$$ having an infinite radius of convergence, does this series expansion hold for all $x \\in \\mathbb R$? Prov... | 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... | BCC |
[
{
"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... | \frac{d^2r}{dx^2}*\left(\frac{dx}{d\beta}\right)^2*\left(\frac{d\beta}{dt}\right)^2+\frac{dr}{dx}*\frac{d^2x}{d\beta^2}*\left(\frac{d\beta}{dt}\right)^2+\frac{dr}{dx}*\frac{dx}{d\beta}*\frac{d^2\beta}{dt^2} |
[
{
"content": "In a building with 1,800 light bulbs, the lifetime of each bulb (in days) is modeled as a Poisson process with an expected lifetime of 200 days. Calculate the probability that at most 10 bulbs fail on any given day.",
"role": "user"
}
] | 0.706 |
[
{
"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... | 0.11 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... | 225 J |
[
{
"content": "Let $\\mathbb{R}[x]$ denote the ring of polynomials in $x$ with real coefficients. Determine the nature of the quotient ring $R=\\mathbb{R}[x]/(x^4+4)$. Is it:\n(a) a field\n(b) an integral domain, but not a field\n(c) not an integral domain, but has $0$ as the only nilpotent element\n(d) a ring w... | C |
[
{
"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... | $8,486 |
[
{
"content": "Evaluate the limit \\( \\lim_{R \\to \\infty} \\int_{-R}^{R} \\int_{-R}^{R} e^{-(x^2+y^2)} \\, dx \\, dy \\) using an approximation for the error function.",
"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... | 67.52 m/s |
[
{
"content": "Using the transformation \\( u = \\frac{w}{y} \\) in the partial differential equation:\n\\[ x\\frac{du}{dx} = u + y\\frac{du}{dy} \\]\nfind the form of the solution for the transformed equation, expressed as \\( w = ? \\).",
"role": "user"
}
] | w = F(xy) |
[
{
"content": "Determine whether the inequality \\( m - n + 1 \\leq \\varphi(n)\\varphi(m) \\) holds for any two natural numbers \\( m \\) and \\( n \\), where \\( \\varphi(n) \\) is Euler's totient function.",
"role": "user"
}
] | No |
[
{
"content": "Determine whether the following conjecture is true or false: For any subset $A$ of a metric space $(M,d)$, the diameter of $A$ is equal to the infimum of the set $\\{\\rho>0;A\\subset B[a,\\rho/2],\\forall a\\in A\\}$.",
"role": "user"
}
] | False |
[
{
"content": "George has a quadratic of the form $x^2+bx+\\frac13$, where $b$ is a specific negative number. Using his knowledge of how to complete the square, George is able to rewrite this quadratic in the form $(x+m)^2+\\frac{1}{12}$. What is $b$?",
"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... | 56.16% |
[
{
"content": "If a function $f$ is Riemann integrable on $[a,b]$ and \\( \\int_{a}^{b} fg = 0 \\) for all functions $g$ that are continuous on $[a,b]$, does it imply that $f(x) = 0$ at all points where $f$ is continuous?",
"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... | $140,799.774 |
[
{
"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... | Total Cost = $108,830 + $0.50 * Fleet Miles |
[
{
"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... | 9676 |
[
{
"content": "Determine the points where the curve given by the equation \\[ 4\\frac{x+2}{\\sqrt{ (x+2)^{2}+y^{2} }}-\\frac{x+1}{\\sqrt{ (x+1)^{2}+y^{2} }}=3 \\] intersects the y-axis.",
"role": "user"
}
] | (0, 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... | L^2= (l(l+1) h^2 and Lz= m h, where m= -l, -l+1, . -1..0....1,2...l and h is h/2pi |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} \\sqrt{2-2\\cos{t}} \\, dt \\).",
"role": "user"
}
] | 8 |
[
{
"content": "In an $n \\times n$ grid filled with $n^2$ distinct real numbers $a_{ij}$ (where $i, j = 1, 2, \\ldots, n$), determine the relationship between the following two numbers: Let $x$ be the smallest number among the maximum numbers from each row, and let $y$ be the largest number among the minimum num... | x \geq 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... | {
"Department": ["Books", "Magazines", "Newspapers", "Total"],
"Sales": ["$495,000", "$198,000", "$207,000", "$900,000"],
"% of total sales": ["55%", "22%", "23%", "100%"],
"Purchase Orders": [516, 360, 324, 1200],
"% of total purchase orders": ["43%", "30%", "27%", "100%"],
"Allocation of advertisement and purch... |
[
{
"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... | 35.8 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... | 74.89 |
[
{
"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 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... | 5.29e-23 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... | 4692.31 |
[
{
"content": "Find the probability distribution of the random variable $T = X^2 + Y^2$, where $(X, Y)$ is uniformly distributed over the unit disk.",
"role": "user"
}
] | 1 |
[
{
"content": "Find the simplified form of the infinite series \\(\\sum_{n=0}^\\infty \\frac{n(n+1)(n+2)}{n! + (n+1)! + (n+2)!}\\).",
"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... | 0.63 MeV |
[
{
"content": "A lane runs perpendicular to a road that is 64 feet wide. If a pole 125 feet long can be carried horizontally from the road into the lane, what is the minimum width of the lane?",
"role": "user"
}
] | 27 |
[
{
"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... | Average Total Cost |
[
{
"content": "Evaluate the improper integral \\( \\int_{1}^{+\\infty}\\frac{1}{\\sqrt[x]{e}}\\,dx \\).",
"role": "user"
}
] | \infty |
[
{
"content": "Calculate the degree of the field extension \\( \\mathbb{Q}(\\sqrt[80]{43},\\sqrt[84]{43})/\\mathbb{Q} \\).",
"role": "user"
}
] | 1680 |
[
{
"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... | 86.014 ksi |
[
{
"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... | 0.534 |
[
{
"content": "Determine whether the sequence \\( x_n = (\\sin(n), \\cos(n), 1 + (-1)^n) \\) in \\( \\mathbb{R}^3 \\) has a convergent subsequence.",
"role": "user"
}
] | Yes |
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