I like it :-)

Though it seems to work only if one accepts the new, strange handling for Pi and floats (thus not setting kernelopts(floatPi=false) )

@phil2 

I checked that FAQ page.

On Windows .. \jre\bin\maple.exe exists only for Maple 18 and not beyond (using 32 bit versions of Maple)

PS: where I find it a quite strange answer anyway, roughly it says "if we want access then give way"

Thank you, Kitonum, I like it!

May be it can be accompanied by an automated plot for the boundary (listing the "corners" as well). If it would be animated then one could "see" that no error was made in the sequence for the input. And perhaps some check (in the routine) whether the overall curve is closed. "Non-selfintersecting" I would  still leave to the user.

here is some screen shot

You have something like a.b in your first equation sol1 - what should that mean?

I transformed the 2F1 by 1/x (after looking at ranges) and finally got some signum(r*3^(1/2)+2*k-2*r), it seems to result in a numerical singularity.

Anyway: I failed to find the integral with Maple and you may stay with MMA for it.

I played with it (though I do not see what that integral should be good for ...) and I think the singularity is along r*3^(1/2) + 2*k - 2*r (some branch cut?). Not caused by a slow 2F1 (at infinity), I suppose.

PS: the discussion which notion in MMA corresponds to what in Maple may be a own topic or worth a question in some MMA forum. As far as I remember old contributions in the usenet by Fateman the models are not directly comparable. No need to put pressure on a new member.

Looking at the data plot that might be 2 periods (or a sum of 2 of such functions)

Best would be to re-type it using Maple's notation - you have to learn that.

I guess you want the value of some bivariate normal distribution (numerically - then you have to provide numbers first for the parameters, else it is not a numerical task).

@acer you are right - forget it

Remark aside: 1 Mio characters ~ 200 pages

@vv yes, you are right - I always forget that very option

You may convert to elementary oder StandardFunctions in that case. Though you may have to simplify (by hand), I do not have a recipe at hand for those "half integer" 2F1.

PS: I think that is not too difficult to numerical compute 2F1 here (even outside of Maple): the variable z = 1/(cosh(x)^2) is between 0 and 1. Between 0 and 1/2 one can compute 2F1 by its series. Else using Abramowitz 15.3.6 with w = 1 - z gives some 2F1, where the new variable w is between 0 and 1/2 plus some GAMMA (due to the constellations of the parameters). For z=1 it is some GAMMA.

Does the following variation work?

fe11_1 := evalf(abs(-piecewise(1 <= p and p <= 9,
 9.310043871-1.372270968*p+0.6222709675e-1*p^2, 0)
 +
 exp(-(1/40)*p*ln(3)-(1/4)*p*ln(2)+(1/40)*ln(3)+(1/10)*ln(p)+(13/4)*ln(2)))):
 
simplify(%) assuming 0<p;
f:=convert(%, rational);

Int(f, p = 1 .. 9);
simplify(%) assuming 1<p,p<9;
evalf(%);

restart;
assume(a > 0, a < 1);
A := Int(ln(-a^2*x^2+1)/sqrt(-x^2+1), x = 0 .. 1):
res := value(A);

about(a);
about(A);

Originally a, renamed a~:
  is assumed to be: RealRange(Open(0),Open(1))

Int(ln(-a^2*x^2+1)/(-x^2+1)^(1/2),x = 0 .. 1):
  nothing known about this object