This will plot the half circle.

Download Half_Circle.mw

Set e to be local is one way to suppress the warning.

local e
                            

a := e^5;
 

e := 2;
                        

a;
                               32

This is not as efficient as the other solutions. It just shows more of the steps involved.
 

Download Parabola_from_vertex_and_line.mw

I deleted my original answer to correct my solution. This is not as efficient as @Rouben Rostamian . It just expands out the steps involved.

Download equations_of_4_lines.mw

If you have any questions just ask.

Download equations_of_4_lines.mw

This post might be of some help to you Solving multi-span Euler beams with the Method of Lines - MaplePrimes

solve(x^4-x^3-3x^2-x+12,x)

This will give you the vlues of x

if you just want numerical answers.

fsolve(x^4-x^3-3x^2-x+12,x)

Hope this helps

Here are two possible ways. Solve the equation before the variables are assigned. e.g. xb:=1000

You can then assign the variables.

or

Use eval and locally give the variables values.

Note your equation has "ab" eb=ab*yb*db*x but "ab" was not assigned you used "xb" so I changed the equation to that.

Download Maple_prine_solve_ans.mw

 This is a way to add elements to a list. 

op[L] removes the brackets from the list. so you get 3,5,7,-6,4,2 to start with. Then ,i^2, i^3 tags on 1,1. The the [   ] reforms a  list. So after 1st loop you now have L as [3,5,7,-6,4,2,1,1]. and it continues

Download Loop_List_Add_to.mw

eq := 2*exp(-2*t) + 4*t = 127:

I am not at Maple PC  at the moment.

But looking at the equation,

we see that this your equation isequivalent to exp(-2t) +2t=63.5

as a first approximation 2t=63.5

so t =31.75

exp(-2x31.75) is going to be very small. i.e 5.9000905*10^-29 (from my TI-68 calculator)

Hope that helps.

Look up the " is " command. Using it with the  " if " command works to evasluate you conditions. Plus a few corection to you code as @tomleslie did.

potfeld := (x, y) -> 1/sqrt(y^2 + x^2);
for i to 5 do
    for j to 3 do 
       if is(sqrt(i^2 + j^2) <> 0 and sqrt((i - 2)^2 + j^2) <> 0 and potfeld(i, j) < 3) 
        then 
           P[i, j] := plots:-arrow(<i, j>, <D[1](potfeld)(i, j), D[2](potfeld)(i, j)>); 
            else P[i, j] := plots:-arrow(<i, j>, <0.1, 0.1>); 
      end if; 
    end do;
end do;
Pseq := seq(seq([P[k, l]], k = 1 .. 5), l = 1 .. 3);
plots:-display(Pseq, view = [1 .. 5, 1 .. 3], scaling = constrained);

The question you have asked requires a decent bit of study. 

I googled "Transformations to hyperbolic plane in Maple"

There are probably many more. 

Hyperbolic Patterns index page (umn.edu)

Hayter_Hyperbolic_report.pdf (dur.ac.uk)

Geometry of Curves and Surfaces with MAPLE - Vladimir Rovenski - Google Books

This one I did actually do several years ago.

Esher’s Limit Circle IV rendered on the complex upper half-plane | Open System - Ark's blog (arkadiusz-jadczyk.eu)

Maple doesn't seem to have that formatting at present. You could try and use a single cell table scaled to the correct width.

Not really a plesent solution I admit.

 

Table_Approx_A4.mw

You need a space or a multiplication * between the R and bracket. Then it solves.

solve(R*(sigma + mu)/nu = (N*b + R*sigma)/(nu + mu), R)

R(...) is a function.

Hope this helps

Would this be acceptable as the sum converges
My internet is faulty at present so I can't get the document to display.

restart;

fd := j -> 256/3*j^5*(j - 1)^(2*j - 4)/(j + 1)^(2*j + 4);
S := x -> sum(fd(n)*ln(1 - 1/n^2), n = 2 .. x);
plot(S(x), x = 2 .. 20);
fd(10);
                             "(->)"
evalf(S(10));
for x from 2 by 5 to 200 do
    x, evalf(S(x));
end do;

Download MP_sum.mw