integrate(sqrt(1+cos(x)^2),x)



see
http://www.math.utexas.edu/pipermail/maxima/2013/034407.html

*On Fri Nov 1 10:40:48 CDT 2013*
> Raymond Toy writes:

> Don't leave us hanging! What serious problems did you encounter in
> computing the numerical values?


 For example:

(%i1) F:elliptic_e(x-%pi/2, -1);
(%o1) elliptic_e(x-%pi/2,-1)
(%i2) ev(F,x=%pi);
(%o2) elliptic_ec(-1)
(%i3) float(%), numer;
Maxima encountered a Lisp error:

Error in PRINT-OBJECT [or a callee]: Bind stack overflow.
Fast links are on: do (use-fast-links nil) for debugging
Broken at CONDITIONS::INTERNAL-ERROR-FUNCTION-NAME.  Type :H for Help.
 1 (Continue) Maxima top-level
 2 (Abort) Return to top level.
dbl:MAXIMA>>


(%i1) wxbuild_info()$
wxMaxima version: 13.4.0
Maxima version: 5.31.2
Maxima build date: 2013-10-07 23:05:06
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8

best

Aleksas D