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Let $\sigma$ be the surface of the solid $G$ that is enclosed by the paraboloid $z=1-x^{2}-y^{2}$ and the plane $z=0 .$ Use a CAS to verify Formula ( 1) in the Divergence Theorem for the vector field $$ \mathbf{F}=\left(x^{2} y-z^{2}\right) \mathbf{i}+\left(y^{3}-x\right) \mathbf{j}+(2 x+3 z-1) \mathbf{k} $$ by evaluating the surface integral and the triple integral.

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