Posting the worksheet would be helpful; use the green arrow button at this site. 

Try replacing e^(-3*x[i]) with exp(-3*x[i]).

@Carl Love Am wondering how a user could find this functionality just using Maple's help.  Given just the idea of using subset with the is procedure it would be difficult to find the technique unless you were aware of SetOf and RealRange, i.e. you already had a good idea for a solution.  

Don't have an answer.  Here's a simple way to illustrate the problem.

plot(sin, 0..2*Pi, 'style=pointline', 'legend'=["a plot"], 'symbol=[solidbox]', 'numpoints'=20)

Note that the plotted line effectively changes with numpoints; set numpoints to 200 and the line will appear quite thick.  To mimic that effect, the plot routine might have to generate the legend by essentially plotting it.

@Carl Love I agree and had the same question.  Submitted it as a request for enhancement.

@Art Kalb Execute showstat(`expand/conjugate`) to see the function that is evaluated.  Note that the first conditional is

if b::('Or(`*`,`+`)') then 
   map(conjugate, b) 
elif 
   ...
end if;

If, as in your case, the b is a sum of products, the distribution will only occur over the sum.

One way to debug this is to edit the startup code (click the Edit menu then select Startup Code) and insert the line stoperror('all'); as the very first line.  Then save the startup region and the worksheet, close the worksheet and reopen it.  When the error occurs the debugger will be launched. In the debugger box ("Enter a debugger command:") enter args to see the arguments passed to `evalf/min` (assuming that was the procedure that raised the error).   

@NeraSnow A helpful to debug this is to replace mod with the neutral operator &mod.  For example,

a := i -> (1025 - 2^(10 - 2^i))^(-1) &mod (1025 - 2^(10 - 2*2^i)):
a(3);
          1021^(-1) &mod (65599/64)

@Carl Love As you noted, the help page for plots:-display doesn't mention that it can handle a bare sequence of plots.  I have verified that there are tests in place to verify that, so it should be relatively safe to use.  Note that you can intersperse the plots with options.  For example

(plots:-display)('axes=boxed', plot(sin), 'title'="Sine and Cosine",  plot(cos));

The call to int is raising

Error, (in int/ellalg/hermite) unexpected square free base 17*_z^2+6*_z*2^(1/2)-2*_z+5+2*2^(1/2)

If the code is modified to call int again, the second call will occasionally run for as long as I care to wait, but other times will succeed in a few seconds.

The mw file is badly formatted.  If you export it as an mpl file (Maple Input Format), the third arguments (eta) in the last two function calls do not exist.  Am guessing there is a weird character in the input.

No file was attached to the question.

I see you've corrected that.

@C_R Just to check, I restored the use of the default page in my Maple 2023, then restarted my linux machine and launched standard Maple.  Didn't notice any obvious slowness when dealing with the default opening page. 

@jalal To remove the two inner circles, add option grid=[0,13].

@C_R I'm not familar with int, but some of the internal procedures, called here, have option cache. While I don't expect that to matter when an error occurs, it's possible that a value could be saved and then later reused without having to attempt the computation that raises an error.  Would have to look closer.

A  problem is the omitted multiplication signs. You should use

   v1 := sin(c)*sin(a)*(a-b);
   v2 := sin(c1)*sin(a1)*(-a+b)