Okay so I found two solved examples (attached).
The first one says:
F (x, y, z) = (y, âˆ’x, z) and P is the bottom part of the surface: z^(x^2+y^2), x^2+y^2<2. Find the flux.
The second one says: F(x,y,z) = (z*e^(y^2), x^2+1, z). P is bottom part of the spherical cap: x^2+y^2+(z-5)^2=25...