Maple : Is it really that hard to realize that sin(pi)=0 ?!

I have an annoying problem in Maple.

I wanted maple to calculate the taylor series of f(x), while:

and so I wrote :

f := (int(exp(x*cos(t)), t = 0 .. pi))/(2*pi)

p10 := taylor(f, x = 0, 11)

And I got an answer that involved multiplying by . I must change all these into zeros, so I tried to use the 'subs' command, or to simplify, even 'simplify trig', but it didn't change a thing.

What can I do in order to get a simple answer?

Thank you :)