Use the Divergence Theorem to evaluate

${\displaystyle \underset{S}{\overset{\phantom{}}{}}}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}F*NdS$

and find the outward flux of $F$ through the surface of the solid $s$ bounded by the graphs of the equations. Use a computer algebra system to verify your results.

$F(x,y,z)=(x{y}^2+cosz)i+(x^{2}y+sinz)j+e^{z}k$

$s$:$z=\frac{1}{2}\sqrt[\phantom{2}]{x^2+y^2},z=4$

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