r:= sin(x)+x*cos(x) < 1/2;
f:= piecewise(r, sin(x), cos(x));

Int(f, x=-1..1); value(%); returns un-evaluated, it seems that a condition fct(x) is an issue

tst0:=abs(sin(x)+x*cos(x)) = 1/2;
solve(tst0, useassumptions) assuming 0<x,x<1; # no solution
fsolve(tst0, x=0..1); # gives a numerical value

In the standard interface (and on Win): menubar / File / Export as opens a dialog window.

There one chooses directory location, file name and file type. The file type can be selected from a list where RTF is the very last entry (scroll in case you can not see it).

It works the same way as exporting a sheet as PDF.

I export the file as *.rtf or as *.html which gives me reasonable quality for the pictures. Processing depends a bit on the text program.

As far as I understand (through the last link) it is an asserted solution for pricing amercan options (without dividend - hm ...),

www.alexbraunstein.com/Untitled.pdf, http://alexbraunstein.com/scripts/ and there  American Option Valuation code  in Phyton

I am not aware of the concurrent state of discussion but suggest you ask first at https://forum.wilmott.com/ and http://www.nuclearphynance.com/ (after having some some search on those forums).

Do you know or guess any (rough) value in the plotrange?

MP_220736.mws

I perhaps do not fully understand the question, but this may be the answer:

Digits:=15;

f := x-> exp(-(1/2)*x^2)/sqrt(2*Pi);
f(x)*f(y)*x*x*'abs'(x+y);
convert(%,piecewise,x):
convert(%, Heaviside): simplify(%); # <-----------
Int(%,x=-infinity..infinity,y=-infinity..infinity);
value(%); #lprint(%);               # almost immediately
evalf(%);

                             3/Pi^(1/2)

                         1.69256875064326

# I had no patients to wait for numerical evaluation of the integral (*)
 

Int(Int(1/2*F(1/2*v+1/2*u,-1/2*v+1/2*u),
  u = -infinity .. infinity),v = -infinity .. infinity);
task:=eval(%, F = '(x,y) -> (f(x)*f(y)*x^2)*abs(x+y)');

st:=time():
evalf(task);
`seconds needed` =time() - st;

                           1.69256875064327

                        seconds needed = 6.225

'piecewise' for that needs ~ 26 sec

(*) but one can manage it as follows
g := convert((f(x)*f(y)*x^2)*abs(x+y), piecewise, x):
g:=simplify(%);

task_2dim:= Int(g, x = -infinity .. infinity,y = -infinity .. infinity,
  method=_CubaCuhre, epsilon=1e-8); # accept some relative error

st:=time():
evalf(task_2dim);
`seconds needed` =time() - st;

                           1.69256875069424

                       seconds needed = 11.716

You may try to use 'Heaviside' instead (please note that Heaviside(0) has
to be defined in case it is needed):

f(x)*f(y)*x^2*abs(x+y); # the integrand
convert(%,piecewise,x);
convert(%, Heaviside);
simplify(%);        # just to avoid multiple calls
int(%,x=-infinity..infinity,y=-infinity..infinity);

                                  3
                                -----
                                  1/2
                                Pi

Perhaps (here) the best is to use a change of variables x+y=u, x-y=v.
I am not aware that Maple supports it directly (*), here it is:

Int(Int(F(x,y),y = -infinity .. infinity),
  x = -infinity .. infinity) =

Int(Int(1/2*F(1/2*v+1/2*u,-1/2*v+1/2*u),
  u = -infinity .. infinity),v = -infinity .. infinity)

where F = your original integrand.

For that also numerical evaluation is fast.

But as others already noted: no need to convert to piecewise here
(exhibiting a bug)

(*) PS: Using IntegrationTools[Change] refuses to give the new integration
bounds (since in general that formula expects a rectangle), but here we
have a linear transform, so this is the full plane again, a rectangle.

Yes.

A more invariant formulation is that hypergeom([1/3, 2/3],[3/2],w)
satisfies a cubic equation and task = picking a specific 'root'.
The equation follows from the ODE approach, this_2F1 = algebraic.

4*h^3*w-27*h+27:

0='eval'(%, h=hypergeom([1/3, 2/3],[3/2],w));
convert(%, StandardFunctions):
convert(%, expln): evala(%): # gives 0
is(%);

             3               |
     0 = (4 h  w - 27 h + 27)|
                             |h = hypergeom([1/3, 2/3], [3/2], w)

                                 true

On the other hand one has

4*h^3*w-27*h+27;
eval(%, w=27/4*z^2*(1-z));
S:=[solve(%, h)];
#plot(%, color=[red,blue,green]);

   S := [1/z,
          1/2*(+1-z+(-3*z^2+2*z+1)^(1/2))/(-1+z)/z,
         -1/2*(-1+z+(-3*z^2+2*z+1)^(1/2))/(-1+z)/z]

hypergeom([1/3, 2/3],[3/2],27/4*z^2*(1-z)):
'eval(%, z=2)'; convert(%, StandardFunctions): evala(%);

                                 1/2

"Hence" one has it as S[1] = 1/z

This is similar to the answers given by vv and Kitonum.

Plotting S "explains" why 1 < z (i.e. w < 0).

I forgot the definition, find it now in the post.
The f is for defining the DE.

The picture does not say "distance matrix". The shown distances / routes may be be weighted ('penalty, costs'). No ?

a := 0.76;
#a:=0.8;
eq1 := 2*cot(a*sqrt(2*E)) - (2*E-5.4)/(sqrt(E*(5.4-E)));
EQ:=convert(%, rational);
solve(%, E);
[allvalues(%)]; evalf(%);

# or RootOf(EQ, E); [allvalues(%)];

added: E=0 is a bit strange anyway ...

Sorry, I have no other suggestion.

I once played with connecting Maple and Excel, but I do not use it.

In your case I would work with functions and procedures, store them in some
*.mpl file (= pure ASCI text). Using "read" in Maple provides it. That avoids
the usage of modules amd should work for all versions.

If you have only a small amount of data then you can work with that directly.
If one has large data sets (say measured data) then you can use import/export
=read/write data files.

PS: you do not need "makeproc" for those 2 functions, you just write them down.

I do not understand it - if you do not have some special requests (high precision, complex values or similar, caring for singularities ... ) all that can be done in Excel using VBA. Where I guess that your "x(t)" is a function of t (and Excel can calculate it)

Your "GeometricData" are parameters - either being feed to the functions(s) itself or being set as 'globals' in VBA.

Note that "portable" is relative: you always would need to have Maple installed.

@Spinosaurus just try it as described, may be using the example covered by Kitonium and post you attempt.