Change the return line to

return convert(orbit, list)

The result needs to be a string (or a name), because an integer can't have the leading zeros. Here's how to make the string:

b:= cat("", op~(convert(a, listlist))[]);

TypeTools:-AddType(Point, [realcons,realcons]):
~set:= x-> convert(x, set):
~list:= x-> convert(x, list):

ThreeIneqs:= proc(A::Point, B::Point, C::Point, XY::[name,name])
uses G= geometry;
local p, a, b, c, L, S:= {A,B,C};
     seq(
          (Eq-> `if`(eval(Eq, XY=~p) < 0, 1, -1)*Eq <= 0)
          (lhs(G:-Equation(
               G:-line(L, (P-> [G:-point(a, P[1][]), G:-point(b, P[2][])])(S minus {p})),
               XY
          ))),
          p= S
     )
end proc:

NumbTrue:= proc(S::~list(boolean), Evals::{set,list}(name=anything))
local r;
     r:= is~(eval(S,Evals));
     `if`(has(r, FAIL), FAIL, numboccur(r, true))
end proc:

TwoOrMore:= proc(Tri::~set(Point), P::Point)
local x,y;
     evalb(NumbTrue([ThreeIneqs(Tri[], [x,y])], [x,y]=~P) > 1)
end proc:

Example:
   
TwoOrMore([[2,3], [4,5], [8,2]], [4,4]);

                                          true

You have two errors:

1. Pi must be spelled with capital P and lowercase i,
2. polarplot should be plots:-polarplot.

It can be done with geom3d:-intersection. In particular, if the result of this command is not NULL, then the input objects intersect.

It can be done in two steps:

convert(s, trig);
combine(%);

f:= 3+2*x+y+2*x^2+2*x*y+3*y^2 = 0:
d1:= implicitdiff(f, y, x);

d2:= implicitdiff(f, y, x$2);

This can be simplified substantially using the original expression and simplify with side relations:

simplify(d2, {f});

diff(f(x,y)=exp(2*x+cos(y)), y$3, x$5);

Edit menu => Split or Join => Split Execution Group (F3)

Simply apply command factor to the result returned by intsolve:

intEq:= 2*cosh(x)-sinh(x)-(2-x)= 1 + int( (2-x+t)* phi(t),t=0..x):
Sol:= intsolve(intEq,phi(x)):
factor(Sol);

Try adding the following option to the plot commands:

xtickmarks= [38320= "11/29", 38330= "12/09", 38340= "12/19", 38350="12/29"]

If you have a lot of such plots to do, it may be worthwhile to write a procedure that translates dates from this "Excel format" to a standard format. This can be done with Finance:-AdvanceDate using any known match (such as 38320 = "11/29/2004") as a reference point. The date can be formatted into a string with Finance:-FormatDate.

A search at the Maple Applications Center turned up one hit: here .

Use Zoom factor from the View menu.

Eigenvalues is in the module (package) LinearAlgebra. So, to use it, you need to either load the package with with(LinearAlgebra) or use the module name as a prefix. I recommend the latter. So, change Eigenvectors to LinearAlgebra:-Eigenvectors.

Assign the solution returned by solve to a variable. Like this

Sol:= solve( ...the rest of your solve command);

Then do

f:= unapply(eval(f(x), Sol), x);
g:= unapply(eval(g(x), Sol), x);