prompt list | ground_truth string |
|---|---|
[
{
"content": "Find the value of \\(a > 0\\) such that \\(a^x - x^a \\geq 0\\) for all \\(x > 0\\).",
"role": "user"
}
] | e |
[
{
"content": "[asy] draw((0,0)--(2,2)--(5/2,1/2)--(2,0)--cycle,dot); MP(\"A\",(0,0),W);MP(\"B\",(2,2),N);MP(\"C\",(5/2,1/2),SE);MP(\"D\",(2,0),S); MP(\"a\",(1,0),N);MP(\"b\",(17/8,1/8),N); [/asy]\nIn the accompanying figure, segments $AB$ and $CD$ are parallel, the measure of angle $D$ is twice that of angle $B... | a+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... | 470484.9158 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... | 1611.61 N |
[
{
"content": "Find the function $f$ that is continuous and differentiable for all $x$, satisfying the functional equation $$ f(x+y)f(x-y) = f^2(x) $$ with the conditions $f(0) \\neq 0$ and $f(1) = 1$. What is $f$?",
"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... | 720.2g |
[
{
"content": "Evaluate the integral \\(\\int_0^{2\\pi}\\int_{-1}^1\\int_0^{\\sqrt{1-z^2}} \\dfrac {r}{\\sqrt{r^2 + (z-2)^2}} dr\\,dz\\,d\\theta\\) using cylindrical coordinates.",
"role": "user"
}
] | \dfrac{2\pi}{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... | 48.53 L |
[
{
"content": "Let $E/\\mathbb{Q}$ be a finite dimensional field extension of $\\mathbb{Q}$ with $\\dim E/ \\mathbb{Q} = 6$. Suppose $\\mathbb{Q} \\subset F_1 \\subset E$ and $\\mathbb{Q} \\subset F_2 \\subset E$ are subextensions with $\\dim F_1 / E = 2$ and $\\dim F_2 / E = 3$. Let $z_1 \\in F_1$ and $z_2 \\in... | 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... | 44100 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... | 1.24 Hz |
[
{
"content": "Given a convex quadrilateral \\(ABCD\\) with sides \\(AB=70\\) units, \\(BC=100\\) units, \\(CD=35\\) units, and \\(DA=75\\) units, and the projection of \\(BC\\) onto line \\(AD\\) is 96 units, find the distance \\(MN\\) where \\(M\\) and \\(N\\) are the intersection points of the angle bisectors... | 25\sqrt{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... | -$27,555.94 |
[
{
"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... | 11.51% |
[
{
"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... | $6650 |
[
{
"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... | 0.661 |
[
{
"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... | 1.537 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... | 15.7 m |
[
{
"content": "Determine the value of \\( k \\) such that the parabola \\( u(x) = x + kx(2-x) \\), passing through the points \\((0,0)\\) and \\((2,2)\\), generates a solid of revolution with the least possible volume when revolved about the x-axis between \\( x = 0 \\) and \\( x = 2 \\).",
"role": "user"
... | -\dfrac{5}{4} |
[
{
"content": "Calculate the expected value of \\(\\frac{\\max\\{|X|,|Y|\\}}{\\min\\{|X|,|Y|\\}}\\) where \\(X\\) and \\(Y\\) are independent random variables each following a standard normal distribution.",
"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... | 600 N.m |
[
{
"content": "Determine the number of Hamiltonian cycles in the complete bipartite graph $K_{m,n}$, where $m$ and $n$ are distinct integers.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the space of real-valued processes $X: \\Omega\\times [0,T] \\rightarrow \\mathbb{R}$, with the norm defined by $$\\Vert X \\Vert = \\mathbb{E} [\\sup_{0 \\leq s \\leq T} |X_s| ^2] ^{1/2}< \\infty,$$ is a closed complete metric space.",
"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... | 7.74e5 N/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... | 3.13e10 |
[
{
"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... | -1805.96 kJ/mol |
[
{
"content": "Solve for the real number $x$ in the equation: \\[ 2^{2x} \\cdot 2^{3\\{x\\}} = 11 \\cdot 2^{5\\{x\\}} + 5 \\cdot 2^{2[x]} \\] where $[x]$ denotes the greatest integer less than or equal to $x$, and $\\{x\\}$ is defined as $x - [x]$. For example, $[2.5] = 2$, $[-3.1] = -4$, and $[\\pi] = 3$. $\\{x... | \dfrac{14}{5} |
[
{
"content": "Evaluate the integral: $$\\int_{0}^{\\infty}\\text{sech}^2(x+\\tan(x))dx$$",
"role": "user"
}
] | 1 |
[
{
"content": "Determine the structure of the quotient ring \\( \\Bbb{C}[X,Y]/(Y-X^2) \\). Show that it is isomorphic to \\( \\Bbb{C}[X] \\).",
"role": "user"
}
] | \Bbb{C}[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... | 836kg |
[
{
"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... | 24.5 m/s |
[
{
"content": "In a rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$, where $A A_{1}=2$, $A D=3$, and $A B= 251$, the plane $A_{1} B D$ intersects the lines $C C_{1}$, $C_{1} B_{1}$, and $C_{1} D_{1}$ at points $L$, $M$, and $N$ respectively. Calculate the volume of the tetrahedron $C_{1} L M N$. Express your... | 2008 |
[
{
"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... | 3.84 x 10^3 V |
[
{
"content": "Determine whether a graph with 7 vertices, each having an odd degree, can contain a complete subgraph with 6 vertices.",
"role": "user"
}
] | No |
[
{
"content": "Consider a Banach space $X$ and a bounded invertible operator $S \\in \\mathcal{L}(X)$. Let $X_1$ and $X_2$ be subspaces of $X$ such that $X_1 \\subseteq X_2$. If $S(X_1) = X_2$, is the restriction of $S$ to $X_1$ invertible from $X_1$ to $X_2$? Provide a justification for your answer.",
"role... | Yes |
[
{
"content": "Let \\( f(x) = \\int_2^x \\frac{1}{1+t^4} \\, dt \\) and \\( g(x) = f^{-1}(x) \\). Find \\( \\frac{d}{dx}(g(x)) \\) at \\( x = 0 \\).",
"role": "user"
}
] | 17 |
[
{
"content": "What is the distance between the points with coordinates $(-5,5)$ and $(5,-5)$? Express your answer in simplest radical form.",
"role": "user"
}
] | 10\sqrt 2 |
[
{
"content": "Determine the values of \\( s \\) for which the integral \\( \\int_{\\mathbb{R}^n}\\left(\\frac{1}{1+|x|^2}\\right)^{s}dx \\) converges.",
"role": "user"
}
] | s > \dfrac{n}{2} |
[
{
"content": "Is the set of all linear functions on the interval $[0,1/2]$ an open subset of the space of continuous functions $C[0,1/2]$?",
"role": "user"
}
] | No |
[
{
"content": "Determine whether the following statement is true or false: For a convex and closed subset \\(C\\) of \\(\\mathbb{R}^{n}\\), the intersection of all tangent cones at points in \\(C\\) contains a non-zero element if and only if \\(C\\) is unbounded.",
"role": "user"
}
] | True |
[
{
"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... | $26,702 |
[
{
"content": "In triangle $ABC$ with area 1, point $P$ is the midpoint of side $BC$. Points $M$ and $N$ are on segments $AB$ and $AC$, respectively, such that $AM = 2MB$ and $CN = 2AN$. The lines $AP$ and $MN$ intersect at point $D$. Determine the area of triangle $ADN$. \\( \\text{(Express your answer as a fra... | \dfrac{2}{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... | 0.42 |
[
{
"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... | 207 mL |
[
{
"content": "In how many distinct ways can you arrange visits to 5 places, labeled A, B, C, D, and E, such that each place is visited exactly twice, and place E is never visited consecutively?",
"role": "user"
}
] | 90720 |
[
{
"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... | $170,000 |
[
{
"content": "Evaluate the integral: $$\\int_0^{2\\pi} \\frac{e^{|\\sin x|}\\cos(x)}{1+e^{\\tan x}} \\, dx$$",
"role": "user"
}
] | 0 |
[
{
"content": "Is the 0-error capacity of a 7-cycle known to be of the form \\(7^q\\) for some \\(q \\in \\mathbb{Q}\\)?",
"role": "user"
}
] | No |
[
{
"content": "Let $\\{f_n\\}$ be a sequence of holomorphic functions defined in a domain $D \\subset \\mathbb{C}$. Suppose that $f_n$ converges uniformly to a function $f$. Is $f$ holomorphic in $D$?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the double integral \\( \\iint_R x \\, dx \\, dy \\) using the change of variables \\( x = \\sqrt{u+v} \\) and \\( y = v \\), where the region \\( R \\) is in the first quadrant of the \\( xy \\)-plane and is bounded by \\( y = 0 \\), \\( y = 16 \\), \\( y = x^2 \\), and \\( y = x^2 - 9 \... | 72 |
[
{
"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... | NO2 |
[
{
"content": "Compute the homotopy group \\( \\pi_3(S^2) \\).",
"role": "user"
}
] | \mathbb{Z} |
[
{
"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... | 100 degrees Celcius |
[
{
"content": "Compute the determinant of the matrix $A = I + yx^H$, where $x, y \\in \\mathbb{C}^n$.",
"role": "user"
}
] | 1 + x^H 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... | 3 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... | 200 hours on speeches and 12000 flyers |
[
{
"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... | 1183.38J |
[
{
"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... | 115g |
[
{
"content": "Is there an injective mapping from \\(\\mathbb{R}\\) to the unit disk in \\(\\mathbb{R}^2\\) defined by \\(x^2 + y^2 \\leq 1\\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the double integral \\( I = \\int_0^1 \\int_0^1 \\frac{x-y}{x+y} \\, dx \\, dy \\) over the rectangle \\([0,1] \\times [0,1]\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of integer solutions \\((x, y)\\) to the equation \\(x^3 - y^3 = 271\\), where both \\(x\\) and \\(y\\) are integers.",
"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... | 45.62 L |
[
{
"content": "A grasshopper starts on island $A$ and hops to one of the two other islands, $B$ or $C$, every minute. In how many different ways can the grasshopper end up on island $C$ after seven minutes, given that it cannot hop to the same island consecutively?",
"role": "user"
}
] | 43 |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\int_{0}^{1} x^{n + 1} \\ln(1 + x) \\, \\mathrm{d}x$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following statement is true for two random variables $C_a$ and $C_b$: $$E[C_u] = E[\\min(C_a, C_b)] = \\min(E[C_a], E[C_b])$$",
"role": "user"
}
] | False |
[
{
"content": "Determine the radius of convergence of the series \\( \\sum_{n=1}^\\infty a_n x^n \\), where \\((a_n)_n\\) is a bounded sequence with \\(L((a_n)_n) \\subseteq \\mathbb{R} \\setminus \\{0\\}\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the integral of \\( \\frac{1}{\\sqrt{z^{2}+x^{2}}} - \\frac{1}{\\sqrt{x^{2}+y^{2}}} \\) over a sphere of radius 1.",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the volume of the region in the first octant bounded by the planes \\( x + y + z = 9 \\), \\( 2x + 3y = 18 \\), and \\( x + 3y = 9 \\).",
"role": "user"
}
] | \dfrac{81}{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... | 10.0 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... | 6.57 A |
[
{
"content": "Determine whether the ratio \\( \\frac{\\pi_g(n)}{\\pi(n)^2} \\) has a limit as \\( n \\to \\infty \\), where \\( \\pi(n) \\) is the number of primes \\( p \\) for \\( p \\le n \\) and \\( \\pi_g(n) \\) is the number of Gaussian primes \\( z = x + yi \\) for \\( |x| \\) and \\( |y| \\le n \\).",
... | \infty |
[
{
"content": "Evaluate the integral \\( \\int_0^{100}\\lfloor x\\rfloor x\\lceil x\\rceil \\, dx \\), where \\( \\lfloor x\\rfloor \\) and \\( \\lceil x\\rceil \\) denote the floor and ceiling functions, respectively.",
"role": "user"
}
] | 24997500 |
[
{
"content": "Let \\( A \\) be a 2x2 square matrix with \\( |A| \\neq 0 \\) such that \\( |A + |A| \\text{adj}(A)| = 0 \\). Find the value of \\( |A - |A| \\text{adj}(A)| \\).",
"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... | $42,447.16 |
[
{
"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... | 1163 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... | 606.52 |
[
{
"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... | [Xe]6s^(1)4f^(14)5d^10 |
[
{
"content": "Let \\( \\Pi_1, \\Pi_2, \\) and \\( \\Pi_3 \\) be the planes with Cartesian equations \\( x + 2y + 3z = 5 \\), \\( x - y + 2z = 7 \\), and \\( 3x - 3y + kz = 10 \\) respectively, where \\( k \\) is a constant. Find the value of \\( k \\) given that \\( \\Pi_1, \\Pi_2, \\) and \\( \\Pi_3 \\) do not... | 6 |
[
{
"content": "Given the entire function $f(z) = u(x, y) + iv(x, y)$, where $z = x + iy$ and $f(0) = -1$, with the partial derivatives $\\frac{\\partial u}{\\partial x} = (e^y + e^{-y})\\cos x$ and $\\frac{\\partial u}{\\partial y} = (e^y - e^{-y})\\sin x$, find the value of $f\\left(\\frac{\\pi}{3}\\right)$. Pr... | \sqrt{3} - 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... | positive |
[
{
"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... | $216,481.68 |
[
{
"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... | 832.50 |
[
{
"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... | $x=\frac{ma}{p_x(a+b+c)}$, $y=\frac{mb}{p_y(a+b+c)}$, $z=\frac{mc}{p_z(a+b+c)}$ |
[
{
"content": "Let $D = \\{(x, y, z) \\mid x^2 + y^2 \\leq 1, z = 0\\}$ be a subset of $\\mathbb{R}^3$. Consider the linear transformation $T : \\mathbb{R}^3 \\to \\mathbb{R}^3$ given by $T(x, y, z) = (2x - y + z, x - y + 10z, 3x - 7y + 2z)$. Determine the area of the set $T(D)$. \\( \\text{Express your answer a... | \pi \sqrt{138} |
[
{
"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... | 38.1464 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... | 12.33 |
[
{
"content": "Determine the values of \\(x\\) for which the series \\(\\sum_{n=1}^{\\infty} \\left[(n^3+1)^{1/3} - n\\right] x^n\\) converges.",
"role": "user"
}
] | [-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... | Be4Si2O9H2 |
[
{
"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... | 3.91e-9% |
[
{
"content": "In a triangle $ABC$ with sides $a$, $b$, and $c$ such that $a \\ge b \\ge c$, it is given that \\( \\frac{a^3+b^3+c^3}{\\sin^3(A)+\\sin^3(B)+\\sin^3(C)}=7 \\). Determine the maximum possible value of $a$.",
"role": "user"
}
] | \sqrt[3]{7} |
[
{
"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... | 7.54 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... | 1.405 L |
[
{
"content": "In the context of the Phragmén-Lindelöf theorem, determine if the bound $M$ can be equal to zero.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty}\\frac{(n!)^{\\frac{1}{(n+1)^2}}}{(n+1)!^{\\frac{1}{n(n+1)}}}.$$",
"role": "user"
}
] | 1 |
[
{
"content": "Compute the limit \\( \\lim_{x \\to \\infty} x e^{-x^2} \\int_0^x e^{t^2} \\, dt \\).",
"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... | 3.97 kg and 0.43 kg |
[
{
"content": "All the numbers 2, 3, 4, 5, 6, 7 are assigned to the six faces of a cube, one number to each face. For each of the eight vertices of the cube, a product of three numbers is computed, where the three numbers are the numbers assigned to the three faces that include that vertex. What is the greatest ... | 729 |
[
{
"content": "A triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3. What is the area of the triangle? Provide your answer as a decimal rounded to the nearest hundredth.",
"role": "user"
}
] | 8.64 |
[
{
"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... | 182 V/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... | 25.24 |
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