I was playing with a problem from the Maple NG, one can state it as
  
  Int( arccos(x) / ( 1+x^4) , x=0 .. 1)

Maple 11.02 gives a result, which numerical can not be valid.

Using real (!) partial fractions (Maple uses decomposition over the
complex, no?) I got a similar problem with denominator = parabola
(and continuity over the integration interval):

  Int( arccos(x) / (x^2 - x * 2^(1/2) + 1), x = 0 .. 1)

Some more and time-consuming consuming experiments reduces troubles
to the following example, where symbolics are disproven by numerics:

  restart: interface(version); Digits:=14:

    Classic Worksheet Interface, Maple 11.02, Windows, Nov 10 2007 Build ID 330022

  Ei(1,1/2*Pi*(1+2*k)): 
  %=convert(%,Sum);
  subs(k=0,%);
  evalf(%);

                    Pi (1 + 2 k)
              Ei(1, ------------) = GAMMA(Pi k + 1/2 Pi)
                         2

                             Pi            Pi
                      Ei(1, ----) = GAMMA(----)
                             2            ...

As an example it is shown, how one convert a (simple) trigonometric equation into a polynomial problem and use Maple
to find a symbolic answer for the equation. The idea is to use the so called Joukowsky transform, which maps the circle
to the interval [-1, ... , +1].

I would have liked to simplify the result (as it is real in my case), but gave up. May be others have a good idea for that.

The recipe is quite simple to understand looking at an example (and it is understood best by having paper and pencil to follow it): f:= x -> x^2 the parabola with its inverse g:= y -> sqrt(y). Say you want the integral of g over 0 ... 2, which (here) is the area between the graph and its horizontal axis. That is the same as the area of the rectangle minus the area between the graph of g and the vertical axis, where the rectangle has corners 0, 2 and g(0)= f^(-1)(0) and g(2)= f^(-1)(2). Now recall the geometric interpretation of the compositional inverse of a function: it is reflection at the diagonal.

Usually exporting from classic interface as HTML works quite well (ok, not all the finer things, but with good (!) graphics and it is painless). Now I want to hide input (for readers not used to Maple that might be better), but with M11.02 the input is exported anyway. Any workaround (except using an editor for the HTML result) ?