A boundary that is a vertical line becomes one of the limits of integration.

If there is any hidden code associated with worksheet, then it can be accessed from the menu Edit -> Startup Code. Many (maybe most) worksheets have their code in plain view right in the worksheet.

Here is how to classify binary matrices by their rank over GF(2).
 

Download rank_mod_2.mw

If someone knows how to make this more efficient by using ArrayTools:-Alias or by other inplace operations, I would appreciate seeing it.

How about

(T-> (p-> [T[..-2][], p])~(combinat:-permute(T[-1])[..max(2,nops(T[-1])!)/2])[])~(Tours);

But, there must be a better way to your overall goal. If you describe that goal better, maybe I can figure out a better way.

min({L[ ]} minus {0});

I think that you're having a problem that the other respondents aren't because you're saving the module to a library and they aren't. Global variables aren't part of the module and thus won't be saved unless they are explicitly mentioned. There is no need for global variables. Try this:

MonPackageFonctions:= module()
option package;
local GeometricData, r, l, ModuleLoad:= ()-> SetGeometricData(0.2, 1);
export 
   GammaNum:= xx->
      evalf(eval(Pi-arccos((-xx^2+l^2-r^2)/xx/r/2), GeometricData)),
   psiNum:= xx->
      evalf(
         eval(
            -arcsin(sqrt(-(xx^4-2*xx^2*l^2-2*xx^2*r^2+l^4-2*l^2*r^2+r^4)/xx^2/r^2)/2/xx/l),
            GeometricData
         )
      ),
   SetGeometricData:= proc(r::algebraic, l::algebraic)
      GeometricData:= [thismodule:-r= r, thismodule:-l= l];
      NULL
   end proc
;
   ModuleLoad()
end module:

This exports a procedure that lets you set the GeometricData externally but also uses r= 0.2 and l=1 as defaults.

If the file is named myfile.bat then do

system("myfile.bat");

There are many possibilities. The criteria are mostly aesthetic. How about this?
 

Download Tours.mw

In differential equations in Maple, the dependent variables must always be used in functional form, i.e., x(t) and y(t) rather than x and y. Therefore, your code should be changed to

with(inttrans);
eq5 := diff(x(t), t)+diff(y(t), t$2) = 5*exp(2*t);
eq5s := laplace(%, t, s);
eq6 := diff(x(t), t)-x(t)-(diff(y(t), t))+y(t) = 8*exp(2*t);
eq6s := laplace(%, t, s);
solve({eq5s, eq6s}, {laplace(x(t), t, s), laplace(y(t), t, s)});
subs({x(0) = 2, y(0) = 1, (D(y))(0) = 1}, %);
eq3 := invlaplace(%, s, t);

If you make this simple change, then the last line will give you the answer that you're looking for.

A more-sophisticated approach---which might be useful if you want to re-use this operation a lot---is to use the RandomTools package:

RandomTools:-AddFlavor(
   A = module()
   local r:= rand(-90..90);
   export Main:= ()-> (a-> [a, convert(a*degrees, radians)])(r());
   end module
):
randomize():
n:= 4:
RandomTools:-Generate(list(A, n));

P:= [$2..5]:
Tours:= combinat:-setpartition(P):
nops~(Tours);
([1,op]~)~(Tours);

Your equation is an ODE with a parameter, y; it is not really a PDE because there are no derivatives with respect to y. So, it can be solved with dsolve:

restart:
equa1:= diff(u(x), x, x) - y*(1+x):
dsolve({equa1, u(0)=0, D(u)(0)=0});

You can use continued fraction convergents, like this:

Download Continued_fraction_convergents.mw

If your version of Maple is too old to have the NumberTheory package, then exactly the same thing is available in the numtheory package as commands cfrac and nthconver.

You can apply simplify to nested piecewise to convert it to a one-level piecewise:

simplify(m);

eval([x,y,z], L);

Careful, that must be [x,y,z] rather than {x,y,z} lest it won't be an ordered triple.