Use a Computer Algebra System to Compute the Flux Of \mathbf

Multiple Choice

Use a computer algebra system to compute the flux of $\mathbf { F }$ across $S$ . $S$ is the surface of the cube cut from the first octant by the planes
$$x = \frac { \pi } { 2 } , y = \frac { \pi } { 2 } , z = \frac { \pi } { 2 }$$
$\mathbf { F } ( x , y , z ) = 5 \sin x \cos ^ { 2 } y \mathbf { i } + 5 \sin ^ { 3 } y \cos ^ { 4 } z \mathbf { j } + 5 \sin ^ { 5 } z \cos ^ { 6 } x \mathbf { k }$

A) $5 \pi ^ { 2 }$
B) $95 \pi ^ { 2 }$
C) $\frac { 5 \pi ^ { 2 } } { 64 }$
D) $\frac { 95 \pi ^ { 2 } } { 64 }$
E) $\frac { 95 \pi ^ { 2 } } { 32 }$