Can one do that with some 'empty default plot' as well?

What I mean: the plot carrying the color in the given codes must have a range
and that should fit to the actual plot (more or less).

It would convenient if having such independently - is that possible?

W is the equation of an affine hyperplane (perhaps over the Reals or Rationals in dim=28).

For that you can find the orthogonal vector, which gives the full space.

From that conversely you can find the hyperplane as the orthogonal complement
plus the shift off the origin.

Also note that you can do this 'exact' and do not need numerical procedures, since you
actually have an (equivalent) system over the Rationals with integer coefficients:

  1000*W: 
  convert(%, rational);

  -112 - 6 x(4) + 2 x(18) + 4 x(5) + 4 x(22) + 17 x(23) + 12 x(20)
         - x(21) + x(19) + 4 x(24) + 8 x(10) + 10 x(27) + 16 x(28)
         + x(6) + 9 x(25) + 6 x(26) + x(17) + x(7) + 4 x(9) + 6 x(3)
         + 17 x(12) + 2 x(13) + 13 x(14) + 4 x(2) + 3 x(1) + 12 x(15)
         + 6 x(16) + 6 x(11)

May be that is the question (of some homework)?

................

I would not expect, that new software works on old operating systems without pain, if ever - and of course would not really expect that old, commercial products are maintained for such.

But I once tried Maple 9.5 on Vista (think it was in 32 bit because of other SW to be checked, like 'old' MS Office): there was no problem for usual and simple handling classical worksheets. The only thing was: exporting (what ever) did not work and was a way to crash the Maple session.

For posting a series of homework questions without any personal effort
you want to post at other places. Or talk with colleagues as well, who did
follow the lectures. Anyway:

1) Look up the help for ?limit and after scanning that try ?limit/dir.
And try to understand the assertion for the exercise and the task
(I would guess, you are not completely posting it).

2) You got the key word in the task: implicit. Use the help and its
topic search to find something rekated to plotting. Applying to your
example would need to try values like x=-1..1 up to x=-1000 .. 1000.

2b) That's more towards Math: how would you understand the question
and what might be an expected answer?

restart; gc(): interface(version);
a:=Matrix(1..5,1..5,(rand(1..1000))/1000):
b:=a*1000:
b[4,4]; type(%,integer);

  Classic Worksheet Interface, Maple 12.02, Windows, Dec 10 2008 Build ID 377066

                                 858

                                 true

Alternatively to Kamel's answer:

Look up the help for ?odetest, it returns 0, if the solution is valid:

  odetest(sol,deq);
                                  0

Note, that Maple returns an answer directly for y(x) using dsolve(deq),
which you can also get from your (implicit) result:

  isolate(sol, y(x));

                            LambertW(C x exp(-1))
                     y(x) = ---------------------
                                      C

The help can tell you a little bit about that special function LambertW
(or you look for it through Wikipedia).

#if ((a>0) and (b>0) then (c:=2*a, d:=3b, e:=9b)
 if ((a>0) and (b>0)) then c:=2*a; d:=3*b; e:=9*b;
 end if;

Or: do not miss to use brackets and multiplication sign
and stements are ended by ';' or ':'

MMA through WolframAlpha gives a solution for the indefinite integral,
though I neither checked it nor applied it for numerical tests.

Maple12 gives HeunG as well

And some caveat on handling: gamma in Maple is Euler's constant = 0.577..., one should not use it as an arbitrary parameter

I do not want to type it in - but you seem to have typos:

T1 = 1 + fraction and Theta_V = fraction are not the same
T2 has an 'F' in both of the exp, Theta_L has some 'E' and 'F'
and you do not have any 'E' at all in your sheet.

The best you could do is: print out the paper and the sheet
and check inputs using a pencil and/or correcting remarks.

Whatever: it is not a Maple or Math problem, so I stop.

Some remarks:

In any case you should check it with higher precision

And better write S0:= fsolve(..., S...) instead of S:= fsolve(..., S...)

But why should your approach work? Essentially you want T1 = T1 in x=S0,
however you compute S0 in a different way. Are you sure that you did that
correctly?

Moreover you should state for which lecture you need that and from which
book you enclosed the plot.

For me summing is over a set, possibly ordered (i.e. a 'list'), or even empty.

Now:

seq(0^k, k = 0 .. 2);
                               0, 0, 0

seq(`^`(0,k),k=0..2);
                               1, 0, 0

There where some threads around Sum's behaviour, but could not find it (one was with contributions by Alec Mihailovs). The choice is not senseless, but strange if having the basic Math definition in mind (never liked that behaviour)

perhaps you want to solve z^2 = x^2 or z^4 = x^4 for x, or z^8 = x^8?