Question: Tricks/tips to do arbitrary-contour integrals of complex functions in Maple ?

I have started to use Maple to test my calculations for a complex variable course.

The example is a complex integrand, and integration about an ellipse centered at origin.
Integrand has function 

f(z) = z*exp(a*z) / (z²+1)²

C:  z(t) = cos(t) + i*2*sin(t)

where a is a real constant. My idea is shown in the attatched workbook, i.e. 

dz = -sin(t) + i*2*cos(t) dt
g(t) = (-sin(t) + i*2*sin(t)) * f(cos(t) + i*sin(t))
int(g(t), t = 0..2*Pi)

PS, I've done similar code previously, but only for circle contours at center (see attachement)

The analytical answer is pi*a*sin(a), and Maple gives this correct for circular contours, but not for the ellipse.

So, what I'm asking is not how to solve the problem, but how to perform (arbitrary) contour integrals in Maple.

attachForMaplePrime.mw