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pretraining/mathematica/geometry/solids/10160.txt

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+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.725 & 0.192 & 0.96 \\
+ 0.86 & 0.422 & 0.169 \\
+ 0.336 & 0.014 & 0.512 \\
+ 0.936 & 0.781 & 0.886 \\
+ 0.148 & 0.522 & 0.648 \\
+ 0.733 & 0.852 & 0.331 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.13$ 
+Solid Angle: $1.26$ 
+Surface Area: $1.6$

pretraining/mathematica/geometry/solids/12948.txt

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+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.351 & 0.334 & 0.36 \\
+ 0.97 & 0.159 & 0.772 \\
+ 0.883 & 0.917 & 0.11 \\
+ 0.039 & 0.663 & 0.628 \\
+ 0.708 & 0.248 & 0.09 \\
+ 0.629 & 0.007 & 0.808 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.69$ 
+Volume: $0.12$ 
+Solid Angle: $3.56$

pretraining/mathematica/geometry/solids/21774.txt

@@ -0,0 +1,19 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.642 & 0.847 & 0.817 \\
+ 0.278 & 0.125 & 0.206 \\
+ 0.979 & 0.237 & 0.312 \\
+ 0.882 & 0.67 & 0.047 \\
+ 0.966 & 0.059 & 0.576 \\
+ 0.03 & 0.595 & 0.7 \\
+ 0.252 & 0.667 & 0.349 \\
+ 0.361 & 0.372 & 0.966 \\
+ 0.901 & 0.91 & 0.738 \\
+ 0.675 & 0.001 & 0.541 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.27$ 
+Surface Area: $2.33$ 
+Solid Angle: $2.78$

pretraining/mathematica/geometry/solids/24720.txt

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+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.895 & 0.891 & 0.963 \\
+ 0.138 & 0.185 & 0.123 \\
+ 0.101 & 0.646 & 0.598 \\
+ 0.984 & 0.529 & 0.875 \\
+ 0.685 & 0.362 & 0.811 \\
+ 0.025 & 0.055 & 0.424 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.06$ 
+Surface Area: $1.31$ 
+Solid Angle: $0.29$

pretraining/mathematica/geometry/solids/28702.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertex coordinates $\left(
+\begin{array}{ccc}
+ \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & 0 & -\frac{1}{2} \\
+ \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} & 0 & \frac{1}{2} \\
+ \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{4} \left(-1-\sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{4} \left(-1-\sqrt{5}\right) & \frac{1}{2} \\
+ \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{4} \left(1+\sqrt{5}\right) & -\frac{1}{2} \\
+ \frac{1}{2} \sqrt{\frac{1}{10} \left(5-\sqrt{5}\right)} & \frac{1}{4} \left(1+\sqrt{5}\right) & \frac{1}{2} \\
+ -\sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & -\frac{1}{2} & -\frac{1}{2} \\
+ -\sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & -\frac{1}{2} & \frac{1}{2} \\
+ -\sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & \frac{1}{2} & -\frac{1}{2} \\
+ -\sqrt{\frac{1}{4}+\frac{1}{2 \sqrt{5}}} & \frac{1}{2} & \frac{1}{2} \\
+ \frac{1}{4 \sqrt{\frac{10}{55+21 \sqrt{5}+4 \sqrt{5 \left(65+29 \sqrt{5}\right)}}}} & \frac{1}{8} \left(1+\sqrt{5}+2 \sqrt{5-\sqrt{5}}\right) & 0 \\
+\end{array}
+\right)$. Determine the SurfaceArea.
+Answer:
+$\frac{1}{2} \left(8+\sqrt{37+10 \sqrt{5}+4 \sqrt{75+30 \sqrt{5}}}\right)$

pretraining/mathematica/geometry/solids/42406.txt

@@ -0,0 +1,17 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.31 & 0.411 & 0.091 \\
+ 0.437 & 0.053 & 0.027 \\
+ 0.909 & 0.478 & 0.253 \\
+ 0.678 & 0.948 & 0.757 \\
+ 0.819 & 0.957 & 0.207 \\
+ 0.332 & 0.952 & 0.803 \\
+ 0.959 & 0.039 & 0.374 \\
+ 0.043 & 0.056 & 0.847 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $2.94$ 
+Volume: $0.26$ 
+Surface Area: $2.51$

pretraining/mathematica/geometry/solids/47.txt

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+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.663 & 0.98 & 0.878 \\
+ 0.444 & 0.265 & 0.015 \\
+ 0.502 & 0.185 & 0.682 \\
+ 0.143 & 0.61 & 0.536 \\
+ 0.035 & 0.531 & 0.877 \\
+ 0.326 & 0.936 & 0.191 \\
+ 0.528 & 0.804 & 0.379 \\
+ 0.507 & 0.102 & 0.069 \\
+ 0.546 & 0.309 & 0.558 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.68$ 
+Solid Angle: $0.71$ 
+Volume: $0.13$

pretraining/mathematica/geometry/solids/52841.txt

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+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.887 & 0.408 & 0.204 \\
+ 0.398 & 0.889 & 0.931 \\
+ 0.084 & 0.928 & 0.634 \\
+ 0.296 & 0.156 & 0.376 \\
+ 0.139 & 0.978 & 0.924 \\
+ 0.176 & 0.987 & 0.963 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.05$ 
+Solid Angle: $0.21$ 
+Surface Area: $1.09$

pretraining/mathematica/geometry/solids/73587.txt

@@ -0,0 +1,13 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.513 & 0.557 & 0.217 \\
+ 0.514 & 0.515 & 0.567 \\
+ 0.095 & 0.937 & 0.689 \\
+ 0.911 & 0.3 & 0.068 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $0.71$ 
+Volume: $0.$ 
+Surface Area: $0.39$

pretraining/mathematica/geometry/solids/77515.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.614 & 0.345 & 0.178 \\
+ 0.028 & 0.904 & 0.196 \\
+ 0.158 & 0.002 & 0.731 \\
+ 0.953 & 0.169 & 0.886 \\
+ 0.373 & 0.648 & 0.16 \\
+ 0.553 & 0.109 & 0.839 \\
+ 0.692 & 0.396 & 0.204 \\
+ 0.095 & 0.543 & 0.957 \\
+ 0.1 & 0.479 & 0.378 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Surface Area: $1.87$ 
+Solid Angle: $2.86$ 
+Volume: $0.14$

pretraining/mathematica/geometry/solids/78073.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.504 & 0.99 & 0.877 \\
+ 0.116 & 0.971 & 0.786 \\
+ 0.909 & 0.14 & 0.297 \\
+ 0.402 & 0.06 & 0.259 \\
+ 0.54 & 0.88 & 0.455 \\
+ 0.079 & 0.619 & 0.686 \\
+ 0.728 & 0.225 & 0.304 \\
+ 0.166 & 0.077 & 0.718 \\
+ 0.631 & 0.713 & 0.806 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $1.32$ 
+Surface Area: $1.71$ 
+Volume: $0.13$

pretraining/mathematica/geometry/solids/88715.txt

@@ -0,0 +1,5 @@
+Problem:
+A sphere centered at $\{-8.799,0.449,1.41\}$ has radius $5.222$. Estimate the sphere's surface area and volume.
+Answer:
+Surface Area: $342.69$ 
+Volume: $596.52$

pretraining/mathematica/geometry/solids/93844.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.566 & 0.73 & 0.532 \\
+ 0.046 & 0.298 & 0.941 \\
+ 0.009 & 0.643 & 0.439 \\
+ 0.992 & 0.114 & 0.327 \\
+ 0.014 & 0.709 & 0.008 \\
+ 0.496 & 0.095 & 0.121 \\
+ 0.141 & 0.851 & 0.139 \\
+ 0.88 & 0.767 & 0.147 \\
+ 0.443 & 0.107 & 0.384 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Solid Angle: $3.21$ 
+Surface Area: $2.17$ 
+Volume: $0.21$

pretraining/mathematica/geometry/solids/93993.txt

@@ -0,0 +1,18 @@
+Problem:
+A polyhedron has vertices with the coordinates $\left(
+\begin{array}{ccc}
+ 0.036 & 0.352 & 0.729 \\
+ 0.979 & 0.068 & 0.857 \\
+ 0.685 & 0.68 & 0.041 \\
+ 0.094 & 0.789 & 0.804 \\
+ 0.991 & 0.227 & 0.378 \\
+ 0.049 & 0.339 & 0.205 \\
+ 0.476 & 0.548 & 0.011 \\
+ 0.167 & 0.501 & 0.944 \\
+ 0.892 & 0.322 & 0.462 \\
+\end{array}
+\right)$. Estimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p.
+Answer:
+Volume: $0.17$ 
+Solid Angle: $2.63$ 
+Surface Area: $2.08$

pretraining/mathematica/number_theory/relatively_prime/11019.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{87,706,-506\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/11173.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{816,-713\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/11520.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-624,-816\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/13033.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{227,-306,900\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/1359.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-50,-320\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/13772.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{159,864,-166\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/16145.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-911,-300\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/16162.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{532,394\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/19653.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{135,218,202\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/20016.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{388,-749,751\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/21735.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{177,814,983\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/219.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{220,733\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/23059.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{487,704\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/2334.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{402,-475\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/23468.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-291,-516\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/23993.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-352,383\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/25406.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-238,-382\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/26098.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{417,-896\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/28782.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{811,860\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/28843.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-168,253,732\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/3042.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-610,-320\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/31071.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-781,11\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/3116.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-278,809,-813\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/31511.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{614,104\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/32645.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-709,-31,23\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/33505.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{219,93,140\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/34018.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{247,846,-840\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/34288.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-943,-19\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/34366.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{407,-570\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/35370.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-375,-939\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/35836.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-30,13,637\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/3598.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-440,-625\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/37177.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-791,394\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/37428.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{219,-760,482\}$.
+Answer:
+$\text{False}$

pretraining/mathematica/number_theory/relatively_prime/37986.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-323,75\}$.
+Answer:
+$\text{True}$

pretraining/mathematica/number_theory/relatively_prime/38173.txt

@@ -0,0 +1,4 @@
+Problem:
+Are the following numbers relatively prime (coprime)? $\{-636,548\}$.
+Answer:
+$\text{False}$