I am trying to calculate the contour integral of exp(-z/A)/z^{2+n}, for constant A and integer n. Here is the Maple code (forgive me, very beginner Maple user here!):

restart;

f := exp(-z/A)/z^(2 + n);
                                 /  z\
                              exp|- -|
                                 \  A/
                         f := --------
                               (2 + n)
                              z       


op~([singular(f, z)]);
                            [z = 0]
poles := [0];
                          poles := [0]
C := z -> is(abs(z) < 1);
assume(2 <= n);
(2*Pi)*I*add(residue(f, z = a), a = select(C, poles));
                              /   /  z\       \
                              |exp|- -|       |
                              |   \  A/       |
                2 I Pi residue|--------, z = 0|
                              | (2 + n)       |
                              \z              /

You can do this by hand by simply expanding the exponential, but how do I make Maple actually do the calculation? (instead of just answering with "residue...".