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... | The radius of the {eq}O_2^{-}{/eq} anion is 1.48954e-8 cm and the radius of the {eq}Mg^{2+}{/eq} cation is 6.16986e-9 cm. |
[
{
"content": "In trapezoid $ABCD$, points $K$ and $L$ are selected on the lateral sides $AB$ and $CD$, respectively, such that the segment $KL$ is divided into three equal parts by the diagonals of the trapezoid. If $KL$ is not parallel to the bases $AD$ and $BC$, find the ratio of the lengths of the bases $AD$... | 2 |
[
{
"content": "Calculate the average distance between two randomly chosen points from the Cantor set.",
"role": "user"
}
] | \dfrac{2}{5} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $30,050 |
[
{
"content": "Evaluate \\( \\lim_{x\\to 2} \\int^{f(x)}_6 \\frac{4t^3}{x-2}\\,dt \\) given that \\( f: \\mathbb{R} \\to \\mathbb{R} \\) is a differentiable function with \\( f(2) = 6 \\) and \\( f'(2) = \\frac{1}{48} \\).",
"role": "user"
}
] | 18 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 13.28 |
[
{
"content": "Let $T$ and $S$ be diagonalizable linear operators on $\\mathbb{R}^n$ such that $TS = ST$. Let $E$ be an eigenspace of $T$. Is the restriction of $S$ to $E$ diagonalizable?",
"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... | 20833.33 |
[
{
"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 mi/hr |
[
{
"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... | 158 * 10^-9 m |
[
{
"content": "Let $S(n)$ be the sum of digits for any positive integer $n$ (in decimal notation). Let $N = \\sum_{k=10^{2003}}^{10^{2004}-1} S(k)$. Determine $S(N)$. \\( \\text{Provide your answer in a single number.} \\)",
"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... | $77.90 |
[
{
"content": "Given the integral equation $f(x)=\\int_{1}^{2}e^{x-t}f(t)\\,dt$, determine the value of $f(0)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the flux across the surface $S$ of the vector field $F=(x+3y^5, y+10xz, z-xy)$, where $S$ is the hemisphere defined by $x^2+y^2+z^2=1$ with $z \\ge 0$. Use the Divergence Theorem to verify the result obtained using the surface integral.",
"role": "user"
}
] | 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... | 83 tablets |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\rightarrow\\infty}\\int_{2n\\pi}^{2(n+1)\\pi}x\\ln x\\cos x\\,dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Suppose $X$ and $Y$ follow a bivariate normal distribution with parameters $\\mu_X = \\mu_Y = 0$, $\\sigma_X^2 = \\sigma_Y^2 = 1$, and correlation coefficient $\\rho_{X,Y} \\neq 0$. Determine the correlation coefficient between $XY$ and $X$, denoted as $\\rho(XY, X)$. Use the hint that a linear tr... | 0 |
[
{
"content": "Given that $a, b, c > 0$ and satisfy the equation $a^2 + b^2 + 4c^2 = 1$, find the maximum value of the expression $F(a, b, c) = ab + 2ac + 3\\sqrt{2}bc$. \\( \\text{Provide your answer as a single number.} \\)",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "Find the limit as \\( n \\to \\infty \\) of the sequence of integrals:\n\n\\[ I_n = \\int_{0}^{\\frac{\\pi}{2}} \\left(\\tan x\\right)^{\\frac{1}{n}} \\, dx \\]\n\nAfter substituting \\( \\tan x = z \\) and simplifying, the integral becomes:\n\n\\[ I_n = \\int_{0}^{\\infty} \\frac{z^{1/n}}{1 + z^2... | \dfrac{\pi}{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... | Accounts payable Inventories |
[
{
"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... | arctan(3/10 + i/10) |
[
{
"content": "Evaluate the limit: \\[ \\lim\\limits_{x \\to 0} \\frac{x\\cos x - \\sin x}{x^3} \\] without using l'Hôpital's rule or Taylor expansion.",
"role": "user"
}
] | -\dfrac{1}{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... | 109.098y1 |
[
{
"content": "Evaluate the integral: \\[ \\int_{0}^{\\infty}\\dfrac{1-e^{-2t}}{t}\\sin{2t}\\operatorname d\\!t \\]",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Find the eigenvalues of the linear transformation \\(T: \\mathbb{R}^2 \\rightarrow \\mathbb{R}^2\\) that maps the circle \\(C=\\{(x,y):x^2+y^2=1\\}\\) to the ellipse \\(E=\\{(x,y): \\frac{x^2}{9} + \\frac{y^2}{4}=1\\}\\). Choose the correct option: \n(1) \\(1,-1\\) \n(2) \\(3,2\\) \n(3) \\(-3,-2\\... | D |
[
{
"content": "Evaluate the integral \\( \\int _\\gamma (e^{z^2} + \\overline{z}) \\, dz \\) where \\( \\gamma \\) is the positively oriented unit circle.",
"role": "user"
}
] | 2\pi i |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 224 g |
[
{
"content": "If $a_1, a_2, a_3, \\\\ldots, a_n$ are $n$ distinct odd natural numbers not divisible by any prime number greater than 5, then what is the maximum value that $\\frac{1}{a_1} + \\frac{1}{a_2} + \\cdots + \\frac{1}{a_n}$ can be less than? \n\n(a) $\\frac{15}{8}$ \n(b) $\\frac{8}{15}$ \n(c) $\\frac{7... | 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... | 7.80% |
[
{
"content": "Find the minimal polynomial of \\( \\sqrt{2} + \\sqrt{5} \\) over \\( \\mathbb{Q} \\).",
"role": "user"
}
] | x^4 - 14x^2 + 9 |
[
{
"content": "Given that $f(x) + f(1 - \\frac{1}{x}) = \\ln|x|$ for all $x \\in \\mathbb{R} \\setminus \\{0, 1\\}$, find the value of $\\int_0^1 f(x) \\, dx$. \\(f: A \\to \\mathbb{R}\\) where $A$ is the set of all real numbers except 0 and 1.",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | (-1347, 1179, 842) N/C |
[
{
"content": "Find the minimum value of $K$ such that the inequality $|x-y| \\geq K |\\ln x - \\ln y|$ holds for all $x, y \\in (1, \\infty)$. \\(\\boxed{K}\\)",
"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... | Courtesy and respect |
[
{
"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 account with 6% interest compounded monthly will have $13,240.83, and the account with 8% interest compounded quarterly will have $14,871.78. |
[
{
"content": "Evaluate the line integral \\( \\oint_C (x^2-y^2)dx+2xydy \\) using Green's Theorem, where \\( C \\) is the boundary of the region enclosed by the parabolas \\( y=x^2 \\) and \\( x=y^2 \\).",
"role": "user"
}
] | \dfrac{3}{5} |
[
{
"content": "The solid shown was formed by cutting a right circular cylinder in half. If the base has a radius of 6 cm and the height is 10 cm, what is the total surface area, in terms of $\\pi$, of the solid? [asy]\nimport three;\nsize(100);\ndefaultpen(linewidth(.7pt));\ncurrentprojection=orthographic(4,2.5,... | 96\pi+120 |
[
{
"content": "Consider a matrix \\( A \\) with \\( m \\) rows and \\( n \\) columns (\\( m > n \\)) over a commutative ring \\( R \\). If \\( A \\) is left invertible, does it imply that there exists an invertible \\( n \\times n \\) sub-matrix of \\( A \\)? Provide a justification for your answer.",
"role"... | No |
[
{
"content": "Given that $a^4 + a^3 + a^2 + a + 1 = 0$, find the value of $a^{2000} + a^{2010} + 1$. Provide your answer as a single number.",
"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... | Q = 23 |
[
{
"content": "Let $\\{a_n\\}$ be an unbounded sequence of positive real numbers such that $\\lim\\limits_{n\\to\\infty}(a_{n+1}-a_n)=0$. Determine whether there exists a sequence $\\{b_k\\}$ with $\\lim\\limits_{k\\to\\infty}b_k=0$ and $\\sum_{k=1}^\\infty b_k=\\infty$ such that $a_n = \\sum_{k=1}^n b_k$ for al... | Yes |
[
{
"content": "Find the degree of the field extension $[\\mathbb{Q}(\\sqrt{5},\\sqrt[3]{2}):\\mathbb{Q}(\\sqrt{5})]$. Express your answer as an integer.",
"role": "user"
}
] | 3 |
[
{
"content": "Determine the minimum possible number of distinct prime divisors of \\(19^{4n} + 4\\) for a positive integer \\(n\\).",
"role": "user"
}
] | 3 |
[
{
"content": "Determine the values of \\(x\\) for which the series \\(\\sum_{n=1}^\\infty \\frac{n! \\> x^n}{(x+1)(2x+1) \\cdots (nx+1)}\\) converges.",
"role": "user"
}
] | [0, 1) |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 2^+}\\frac{[x]\\sin(x-2)}{(x-2)^2}$$ where [x] represents the fractional part of x.",
"role": "user"
}
] | 1 |
[
{
"content": "Find the partial derivative \\( \\frac{\\partial}{\\partial X} \\text{tr}(XAX) \\), where \\( A \\) and \\( X \\) are \\( n \\times n \\) matrices, and \\( A \\) is a constant matrix. Provide a proof for your answer.",
"role": "user"
}
] | X^\top A^\top + A^\top X^\top |
[
{
"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... | 32.5 m |
[
{
"content": "Find the residue of the function \\( g(z) = \\frac{1 - e^{2iz}}{\\cosh^2(2z)} \\) at \\( z = \\frac{\\pi}{2} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the minimum number of charts required to cover a torus, given that each chart must consist of simply connected open sets.",
"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... | B = \frac{\pi \mu_0I}{L} |
[
{
"content": "A circle with radius 3 is inscribed in a right triangle. Another circle, with radius 2, is tangent to the inscribed circle and both legs of the triangle. What is the area of the triangle?",
"role": "user"
}
] | 84 |
[
{
"content": "Determine the exact value of the covering radius $R_v$ for a face-centered cubic (fcc) lattice, given that the maximum non-intersecting radius of each sphere is $r_c = \\frac{1}{\\sqrt{2}}$. Assume that sphere-sphere overlaps are allowed, and no point in the lattice is outside of a sphere. Express... | 1 |
[
{
"content": "The surface defined by the equation \\( z = x^2 - y^2 \\) is intersected by the plane \\( y = 3x \\), resulting in a curve. Determine the slope of this curve at the point \\( (1, 3, -8) \\).",
"role": "user"
}
] | -16 |
[
{
"content": "Find the radius of convergence of the series \\( \\sum_{k=1}^{\\infty} \\frac{(2k)(2k-2)\\cdots 4\\cdot 2}{(2k-1)(2k-3)\\cdots 3\\cdot 1} z^k \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Find all continuous functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that \\( f(0) = 0 \\), \\( f(2x) \\geq x + f(x) \\), and \\( f(3x) \\leq 2x + f(x) \\).",
"role": "user"
}
] | f(x) = x |
[
{
"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... | 61,132 N/C |
[
{
"content": "If a sequence of functions converges uniformly to a discontinuous function, must all functions in the sequence be discontinuous?",
"role": "user"
}
] | No |
[
{
"content": "The side length of the regular hexagon is 10 cm. What is the number of square centimeters in the area of the shaded region? Express your answer in simplest radical form.\n\n[asy]\nsize(100);\n\npair A,B,C,D,E,F;\nA = dir(0); B = dir(60); C = dir(120); D = dir(180); E = dir(240); F = dir(300);\n\nf... | 100\sqrt{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... | 4% + (8.92% * Beta_1) + (7.41% * Beta_2) |
[
{
"content": "Evaluate the triple integral \\( \\int\\int\\int_R \\cos x \\, dxdydz \\), where \\( R = \\{(x,y,z) \\in \\mathbb{R}^3 : x^2+y^2+z^2 \\le \\pi^2\\} \\).",
"role": "user"
}
] | 4\pi^2 |
[
{
"content": "Find the derivative of the function \\( f(x) \\) defined as follows:\n\n\\[\nf(x) = \\begin{cases} \n\\ln(\\sin(x)) - \\ln(x), & \\text{if } 0 < x < \\pi \\\\\n0, & \\text{if } x = 0 \\\\\n\\ln(-\\sin(x)) - \\ln(-x), & \\text{if } -\\pi < x < 0 \n\\end{cases}\n\\]\n\nDetermine if the derivative ex... | 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... | 30.5 kPa |
[
{
"content": "What is the minimum number of equilateral triangles, of side length 1 unit, needed to cover an equilateral triangle of side length 10 units?",
"role": "user"
}
] | 100 |
[
{
"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... | -17.118 kJ |
[
{
"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... | 1705/3 W |
[
{
"content": "Determine the dimension of the vector space \\( k[x,y,z] / (x, y^2, z^2) \\) over the field \\( k \\).",
"role": "user"
}
] | 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... | push r@416
mov a@400, QWORD PTR rbp-8
mov b@408, QWORD PTR rbp-16
add a@400, b@408
cvtsi2sd xmm0, a@400
movsd xmm1, QWORD PTR.LC0rip
divsd xmm0, xmm1
movsd QWORD PTR r@416-24, xmm0
mov eax, 0
pop r@416 |
[
{
"content": "Consider the equation \\(x^{2007} - 1 + x^{-2007} = 0\\). Let \\(m\\) be the number of distinct complex non-real roots and \\(n\\) be the number of distinct real roots of the equation. What is the value of \\(m - n\\)?\n\n1. \\(0\\)\n2. \\(2006\\)\n3. \\(2007\\)\n4. \\(4014\\)",
"role": "user"... | D |
[
{
"content": "In triangle $ABC$, where angle $C$ is a right angle, the medians $AD$, $BE$, and $CF$ are drawn. The median $AD$ lies on the line $y = x + 3$ and median $BE$ lies on the line $y = 2x + 4$. Given that the hypotenuse $AB$ has a length of $60$, find the area of triangle $ABC$.",
"role": "user"
... | 400 |
[
{
"content": "Determine the radius of convergence of the series \\(\\sum a_n z^n\\), where \\(a_n = \\frac{(n!)^3}{(3n)!}\\). Use Stirling's formula, \\(n! \\sim \\sqrt{2\\pi n}(n/e)^n\\), to find the limit superior of \\(|a_n|^{1/n}\\).",
"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... | 0.5 C |
[
{
"content": "Determine the number of distinct prime ideals in the ring \\( \\mathbb{Q}[x]/(x^4-1) \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to -\\infty} \\sum_{k=1}^{1000} \\frac{x^k}{k!} \\]",
"role": "user"
}
] | \infty |
[
{
"content": "Determine whether a complete metric can be defined on the open interval (0,1) that induces the standard subspace topology.",
"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... | 46.64 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... | 532.05 m |
[
{
"content": "What is the arithmetic mean of the integers from -4 through 5, inclusive? Express your answer as a decimal to the nearest tenth.",
"role": "user"
}
] | 0.5 |
[
{
"content": "If a function \\( f: \\mathbb{R} \\to \\mathbb{R} \\) is not monotonic, must there exist three points \\( x < y < z \\) such that either \\( f(y) < f(x), f(z) \\) or \\( f(y) > f(x), f(z) \\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of real solutions to the equation \\( \\sin x + 2\\sin 2x - \\sin 3x = 3 \\) for \\( x \\in (0, \\pi) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the value of the parameter \\( \\rho \\in [0,1) \\) such that the numerical method \\[ y^{n+1}=y^n+h \\cdot [\\rho \\cdot f(t^n,y^n)+(1-\\rho) \\cdot f(t^{n+1},y^{n+1})] ,\\quad n=0,\\ldots,N-1 \\\\\\ y^0=y_0 \\] has maximum order. Let this value be denoted as \\( \\rho_m \\).",
"rol... | \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... | 58 months |
[
{
"content": "Is a map of fibrant marked simplicial sets a fibration in \\(\\mathrm{sSet}^+\\) if and only if its underlying map of simplicial sets is a fibration in \\(\\mathrm{sSet}\\) with Joyal's model structure?",
"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... | $104,089.40 |
[
{
"content": "Find the value of $k$ such that the fractional part of the number $\\frac{3^{500}}{17}$ is $\\frac{k}{17}$.",
"role": "user"
}
] | 13 |
[
{
"content": "Find the projection of $\\begin{pmatrix} 1 \\\\ 2 \\\\ 3 \\end{pmatrix}$ onto the plane $3x - y + 4z = 0.$",
"role": "user"
}
] | \begin{pmatrix} -1/2 \\ 5/2 \\ 1 \end{pmatrix} |
[
{
"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... | q/2m |
[
{
"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... | 7.07 A |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\rightarrow0}\\frac{(e^x \\sin x- (x+1)\\tan x)}{(x\\log\\cos(x))} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral \\(\\displaystyle\\oint_C\\left(\\frac{1}{\\sin(z)-1}\\right)dz\\) where \\(C\\) is a circle with radius 5, oriented clockwise.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the base \\( b \\) such that the numbers 220, 251, and 304 are three consecutive perfect squares when expressed in base \\( b \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Calculate \\( I'(0) \\) for the function \\( I(x) = \\int_{0}^{2x} f(x-t) \\, dt \\), where\n\\[\nf(x) = \\begin{cases} \\frac{\\ln(1+\\sqrt{2}x+x^2)}{x} & x \\neq 0 \\\\ 0 & x = 0 \\end{cases}\n\\]",
"role": "user"
}
] | 2\sqrt{2} |
[
{
"content": "Determine the number of roots of the equation \\( 2\\cos^{2} \\theta = 1 + 3^{\\sin \\theta} + 3^{\\csc \\theta} \\) in the interval \\([0, 2\\pi]\\).",
"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... | $29,071.16 |
[
{
"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... | 9.769 m/s^2 |
[
{
"content": "Suppose $f$ is an analytic function on the unit disk $D = \\{ z \\in \\mathbb{C} : |z| < 1 \\}$ and continuous up to the closure $\\bar{D}$. If $f$ vanishes on a non-null segment of the boundary, such as $\\{ e^{it}, 0 \\leq t \\leq \\pi/2 \\}$, is $f$ necessarily zero everywhere on the boundary? ... | 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... | $23,428 |
[
{
"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 torque is 65.45Nm if the rod rotates about the center and 261.8Nm if the rod rotates about one end. |
[
{
"content": "Find the operator norm of the linear operator \\( I: C([0,1],\\mathbb{R}) \\to \\mathbb{R} \\) defined by \\( I(f) = \\int_0^1 f(x)\\,dx \\), where \\( C([0,1],\\mathbb{R}) \\) is the vector space of continuous real-valued functions on the interval \\([0,1]\\) with the norm \\( \\|f\\| = \\int_0^1... | 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... | 263 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... | 406000 |
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