You have a path integral, not a line integral (in Maple terminology).

VectorCalculus:-PathInt( 3*y-x, [x,y] = Line(<2,1>, <3,-1>) );


(I'd recommend to compute it by hand too).

Use two pairs of quotes.

evalf(Int(''g(x)'',x=1..2));
evalf(Int(''h(g(x))'',x=1..2));

For the last one you may use:

evalf(Int(h@g, 1..2))

Use a duplicate parameter. Example:

f:=piecewise(a=0, aa*x^2+b, a*x^2+b):
Explore(plot(f,x=-1..1, view=[-1..1,-1.0..4]),
        initialvalues=[a=0, b= 0.0],
        parameters=[ [a, controller=textarea],  #set a=0 to use the slider
                     [aa=1.0 .. 3.0],
                     [b=-1.0 .. 1.0]
                   ]);

combine (or combine/power) does not work for products with symbolic limits.

But if you specify n (e.g. n=10), combine(%, power) gives the desired form.

Use any of the following:

eval(x,ans[2]);
                  
rhs(ans[2][]);
                  
op([2,1,2],ans);

With the default method and precision, Maple approximates wrongly some of the integrals (or does not approximate at all).
To get the correct results, change for example  A[a]:=...

to

A[a] := int(f(x)*g(x,a),x=-infinity..a-1,numeric,digits=20,epsilon=10^(-10));

I think that there are good alternatives.

- For collected terms in an expression see ?LargeExpressions

- The results in your worksheet are easier to read if we use:

alias(alpha=RootOf(_Z^2+5));
alias(beta=RootOf(9*_Z^6-48*_Z^5+30*_Z^3+25));

[this way we have full control on abbreviations]

y(z) = F(z) + int(sqrt(z - sigma)*y(sigma), sigma = 0..z);
intsolve(%, y(z), method = Laplace);

ff:=proc(a)
local aa,sa:=convert(a,set),T,u;
aa:=zip(`[]`,a,[$1..nops(a)]);
for u in sa do T[u]:=NULL od;
for u in aa do T[u[1]]:=T[u[1]],u[2] od;
[seq([T[u]],u=sa)];
end:

ff([[x+y+z],[2*x+y+z],[x-y+z],[2*x+y+z]]);
                       [[3], [1], [2, 4]]

Seems to be a little faster and easier to read.

It's difficult to understand what you are trying to do.

It seems that you want to use the implicit equation of the spiral r = theta  (given in polar coordinates) and to obtain the points of intersection with some line.

1. You forgot  the third equation:  r = sqrt(x^2 + y^2)

2. eq1 is wrong; LHS should be r  (not r^2) . But RHS is wrong too (see below).

The correct implicut equation of the spiral is

(F(x,y) =)     frem(sqrt(x^2 + y^2) - arctan(y,x), 2.*Pi) = 0

But you should not use it; with polar coordinates is much better. Note that e.g. implicitplot  is not able to draw correctly  F(x,y)=0.

If you want to intersect the spiral with a line (say a*x+b*y+c=0), just solve the system

{r = theta,  a*r*cos(theta) + b*r*sin(theta) + c = 0}

It will have an infinity of solutions; you can use solve followed by evalf(allvalues(%))  or RootFinding.

You must define the points first.

with(geometry):
point(F1,0,1), point(F2,4,1);
ellipse(e1,['foci'=[F1, F2], 'MajorAxis' = 8],[x,y]);

draw(e1);

If you can still open other files (.mw ?), it seems that some of your files are corrupted.

Upload one of them here. Or at least inspect its size, complete path, open it with Notepad (if the OS is Windows) and copy here the first few lines.

Logic:-Satisfy is new in Maple 2016. The variable p was forgotten from the local sequence.

As a workaround you can start with
local p
in your worksheet.

restart;
with(Logic):
local p;
p:=5;
Satisfy(x or y); p;
                     {x = true, y = false}
                               5


Edit. Now p is local to your program and the variable altered by Satisfy is :-p

To inspect the coordinates use plottools[getdata]

A:=plots:-implicitplot(x^2+y^2=1, x=-1..1, y=-1..1):
plottools:-getdata(A)[3];  # double click the summarized Matrix

convert(%,list,nested);    # if you really want a list

simplify(eval(x-y+4*z, [x = (u-v)^2, y =  u^2-3*v^2, z = (1/2)*v*(u-2*v)]));
      0

So, the surface is contained in the plane x-y+4*z=0.

(Of course x-y+4*z can be obtained via Groebner.)