evaluate double int over S (e^z) dS

where S is the surface of the sphere x^2 + y^2 + z^2 = a^2

I know dS = a^2(sintheta)(d.theta)(d.phi) using the parametrization

r = (a.sintheta.cosphi,a.sintheta.sinphi,acosphi)

so from there do I just calculate

int int e^(acosphi) a^2(sintheta)(d.theta)(d.phi)

?

many thanks