1) Use Stokes' Theorem to evaluate $$\displaystyle\iint_S\mathrm{curl}~\mathbf{F}\cdot d\mathbf{S}$$ $\mathbf{F}(x,y,z) = xyz~\mathbf{i}+ xy~\mathbf{j}+ x^2yz~\mathbf{k}$. $S$ consists of the top and four sides (but not the bottom) of the cube with vertices $(\pm9,\pm9,\pm9)$, oriented outward.
2) Use Stokes' Theorem to evaluate $$\displaystyle\iint_S\mathrm{curl}~\mathbf{F}\cdot d\mathbf{S}$$ $\mathbf{F}(x,y,z) = x^2z^2~\mathbf{i} + y^2z^2~\mathbf{j} + xyz~\mathbf{k}$. $S$ is the part of the paraboloid $z = x^2+y^2$ that lies inside the cylinder $x^2+y^2 = 25$, oriented upward.
I am pretty much lost.
[ Answering just to reduce lists of questions with no answers; guessing 3-month stale homework answer is of limited use! ]
Stokes' theorem equates { the flux of $\operatorname{Curl}\mathbf{F}$ through any surface $S$ with an oriented boundary $C$ } with { a work integral on $C$ }. The theorem lets you replace a complicated surface $S$ in your integrals with a simpler surface $S'$ as long as the surface normals are pointing so as to give the same orientation for $C$.
In (i) you can replace $S$ by the top face of the cube ($0\le x\le 9,0\le y\le9,z=9$) with normal pointing downward. Picture the cube-without-top shrinking into the region where the top face would be; the surface normal ends up as $-\mathbf{k}$.
If (ii), the boundary $C$ of $S$ is the circle $x^2+y^2=25,z=25$. Imagine $S$ shrinking upward into $S'$, the disc with boundary $C$. The inward pointing normals on $S$ end up as an upward point normal $\mathbf{k}$ on $S'$.