I think I found a bug in MapleV.4(00f).
On the contrary,
which is obviously wrong.
I suspect the bug is in the evalc() command.
The bug is removed with Maple V Release 5. (U. Klein)
Continuing on this theme of Lucca Ciotti (sorry to say it, but Maple is a goldmine if it comes down to errors in branch cuts of complex functions):
The integral of a real function like: log(sin(x)) is of course determined up to a constant. If the integral happens to be explicitly available, this constant may be appear to be complex, and I can understand that if one of the occurring functions is multivalued (and has branches, branch cuts, etc) this constant may jump from one value to another along the x-interval. (This is why it is always tricky to accept a result from int(f(x),x=a..b) straightaway.)
However, the imaginary part of the integral of log(sin(x)) is not piecewise constant on 0..Pi!
Between 0 and Pi/2 it is constant, but it decays linearly between Pi/2 and Pi. (Then along Pi..2 Pi it also grows linearly, but this is how it should, because sin(x)<0, and log(sin(x)) an imaginary constant.)
So there is something more ﬁshy going on ....