$$ \begin{split} F &= \left(x^2, y, \frac{\sin(z)}{z}\right) \\ A &= \left\{(x,y,z) \in \mathbb{R}^3: {x^2\over e^x} + {y^2\over e^{-z}} \le 1 \text{ and } -{\pi\over2} \le z \le {\pi\over2}\right\} \end{split} $$
I'm trying to solve this flux exercise with the usual method, applying the divergence theorem. However I've spent 2 hours trying to find a variable change that makes the domain normal so as to actually calculate the integral. Does anyone have any idea on how to treat $A$? It looks like something you would use elliptical coordinates for but the $e^x$ under $x^2$ really makes it much more difficult to me. Do you have suggestions? Thanks