1. The only Graphics package I have loaded which *ought *to be able to view EPS is GIMP2.8
2. If I save a 3D plot from Maple18 in EPS format, GIMP does not load/render it correctly
3. If I save a 3D plot from Maple 2017 in EPS format, then GIMP loads/renders it correctly
4. This could be a problem with GIMP(?), which wouldn't be experienced with Latex, but since OP is using Maple18, then maybe EPS isn't the best choice.
5. I'm not sure what a standard Latex installation would import, but exporting from Maple 18/Maple2017 as windows metafile (wmf), resulted in pretty nice figures in the viewers (GIMP/Paint) I used

on larger projects - for more or less the same reasons.

However I rarely use cut-and-paste to transfer to Maple. Rather I save from the editor as a ".m" file, and then read that file with a simple 'read' statement in Maple. Works fo me but then everyone finds there own "best practice"

Note that the output of the fsolve() command and the DirectSearch:-SolveEquations() command, do not correspond very well. Hence my original statementt that there are probably several equally viable solutions

Please note that unless you have the DirectSearch package loaded you will not be able to reexcute this worksheet completely

Download solProb.mw

I tried this on

Maple 18
Maple 2015
Maple 2016
Maple 2017

with inconsistent results. As in, for any particular Maple version, sometimes a solution would be obtained and sometimes not! Couldn't check Maple 15, because I only have the above four Maple versions loaded.

Running the DirectSearch:-SolveEquations() command with the 'iterationlimit ' set to 20000, "worked" in all four of the above Maple releases. I use the term "worked" loosely because, whilst the residual mean squared error was always less than 1e-09, the returned variable values varied significantly. This suggests that, for a given numerical error limit, several (different) solutions are possible.

PS The DirectSearch() package is a (free) Maple add-on, available from the Maple Application Centre

Becuase those who write the original code with its embeeded error messages cannot allow for all of the dumb things which users might do. The original error message states

"Error, (in Bits:-GetBits) argument 1, the number, must be a nonnegative integer"

I therefore conclude that whatever you have supplied as "argument 1" is not a non-negative integer. What exactly is difficult?

You original problem statement only has enough equations to deal with the unknowns V[1](t), V[2](t) etc. Tou cannot add arbitrary amounts of unknowns to the same number of equations and hope for a solution.

Simple thought process: I propose to add 100 unknown functions to your four known equations; on you planet I will be able to solve for these 100 unknown functions (or 1000, or 100000, or whatever). There is a link betweennumber of unknowns and number of equations which can never be broken

PS I should apologise to Preben for confusing him with Rouben - I must have had a brain freeze

restart;
with(LinearAlgebra):
K:= ExcelTools:-Import("C:/Users/TomLeslie/Desktop/Feeder4.xls",1,"Names"):
f:=x->`if`(Equal(x,<0|0|0>), NULL, `if`(x[1]=0, "", cat(x[1],x[3]))):
L:=<seq(f(j), j in Row(K, 1..op([1,1],K)))>;

You should bear in mind that if you change the layout of your Excel spreadsheet, then the above may need to change

As wel as the issues pointed out by Rouben, you are seeking to minimise the quantity E( f(x) ).

However as you define the function f(), it will return a single value, for a single supplied argument. However the function E() requires three arguments - so this is never going to work

The first thing you have to appreciate is that Maple 7 is ~20 years old. No-one here has a copy of Maple 7. It is ancient. So the best you are ever going to get is "educated guesses" about how 20-year-old software works. Having got that off my chest, try the following

restart;
with(plots):
with(plottools):
w:=1.5:
lup := line([w,0.9], [w,5.1], color=red, thickness=4):
plt:=plots[implicitplot]((x-1)^4/24+(y-3)^4/10=2, x=w..7, y=0..12,color=red, thickness=4):
op(plt);

The output of the final command (ie op(plt) ) *ought* to be a list (possibly a sequence, maybe something else?) of information about your plot. One of the items in this unknown list/array/sequence/matrix/table/whatever *ought* to be an array/matrix/table/whatever which contains the data points being plotted. All you have to do is to extarct the relevant data item from whatever is returned by the op(plt) command. Ths involves supplying appropriate indices to this command.

So you can start with

op(1, plt);
op(2  plt);
op(3, plt);

until one of them returns the data item which may either be the table/array/matrix which you want, or it contains the table/array/matrix which you want. In the case of the latter then  you need to supply second indices - so if, for example, op(2,plt) above supplies the data table/matrix/array you want along with some other stuff, then you start using

op([2,1], plt);
op([2,2], plt);
op([2,3], plt);

and so on, and so forth. I very much doubt that you will have to use a thrid level of indexing, but I supposes you might.

This isn't rocket science

The file letrot.mws which I uploaded is an executable worksheet - just like the file in your original post.

1. It contains no "images"  png files, or gif files
2. When you state that "plottools does not evaluate to a module" - it did in your original worksheet. What else did you mean by the wittj(plottools) command? And how did commands such as rotate() and polygon() work? All of these are part of the plottools package
3. There is no plottools:-exportplot(FA,p) command; nor does the command A:=plot3d (1,....,image=FA) exist in the worksheet I posted
4. I didn't say  "...all the way back to Maple 2018", I said "all the way back to Maple 18", There is a difference. After Maple 18 came Maple 2015, then Maple 2016, and now Maple 2017

Resaved it as a .mws file

This works all the way back to Maple 18, which is about six years old. Can't check anything earlier because I just don't have any older Maple versions installed).

letrot.mws

Give or take a coupel of significant digits, the answer is {1053.000063 < x, x < 1054.000063}, which you can obtain with

evalf~( solve( [ 3^665/2^x>1,
                          3^665/2^x<2
                        ]
                     )
          );

One can check answers in this range with

seq( [x, evalf(3^665/2^x)], x=1053..1054.1,0.1);

which pretty much confirms that anything between 1053.000063..1054.000063 will work (bearing in mind that the last one or two significant digits may be slightly 'off')

Many matrix operations (eg simple multiplication) are non-commutative. Substituting simple symbols for matrices could therefore get you into all sorts of trouble

Link now works correctly, but whoever devised this update process seems to delight in making things difficult

1. At least the link now has the download files
2. For reasons which escape me, the relevant zip file is downloaded to the folder C:\Users\TomLeslie\AppData\Local\Temp on my machine. My default "downloads" directory is set up to be D:\Users\TomLeslie\Downloads. How you managed to download to the former rathe than the latter escapes me. Why does it matter? Related to my backup strategy: my drive "D" is a data disk which is backed up every night; my drive "C" is the system disk which is only backed up once a week
3. In order to access/unzip relevant information from this file (once located), I have to run winzip with administrator privileges - other wise I can't transfer the relevant Phyics2017.mla file to the relevant folder
4. The InstallationsInstructions.pdf states "Copy the Physics2017.mla file found within the zip that contains the Updated Physics library (where this file you are reading is included) into your Maple system library folder - if the file already exists, overwrite it.". I assume that all users know that this means copy the file to the sub-folder named "lib" within your Maple installation folder
5. The InstallationsInstructions.pdf also states that you can verify correct update by checking the PhysicsUpdate.mw worksheet in the downloaded zip file. The PhysicsUpdate.mw file does not exist in the downloaded zip file. Only simple way I could verify that I had made all relevant updates correctly, was to rerun the OP's original problem and confirm that his/her error had "gone away"
6. How long did it take to igure out/fix all of the above - well for me, about 10mins. For less experienced users, who knows?

@ecterrab 

I spent a coupleof hours on this problem, this morning and (realistically) I got pretty much nowhere. To add to my annoyance you now suggest a download fix, except the page you reference contains no downloads (seems to be for uploads). I tried most of my usual guessing techniques on where the download page might be, and got absolutely nowhere!

Please specify a download link which works!