@Alfred_F Thanks. Changed to maximize.

@Rouben Rostamian  Yes, my plot (and calculation) are wrong. If I change the plot range to 0..40 rather than 0..x__max, I see the plot doesn't come down to the axis; Maple seemed to add a phantom point  in the 0..x__max case. So I see my mistake, and with a recalculated mu to make the plot to come to the axis I get the same value as you did. I've updated my answer and left the other one there for the record.

Thanks!

@Rouben Rostamian  I look forward to it; see what I got wrong. Edit: I figured it out.

@Paras31 If I look at integrand1, you have i; presumably i in exp(i*k*x) is supposed to be I=sqrt(-1), but in k1 you have I for sqrt(-1) and i interpreted as I. In k2 you have i interpreted as i. You need to use one or the other as sqrt(-1) - if using i, then you need to use interface(imaginaryunit=i).

@janhardo Thanks. I solved just the top part, for which the fence length is 50 m, so total fence length, top and bottom is 100 m. I've edited to clarify.

@Alfred_F Thanks; that's clear. (I was confused about why the buyer wanted to spend more money.)

I'm confused. The cost is Int(x*y(x), x=0..xmax) and the area is Int(y, x=0..xmax) and the fence length is L. So the cost and L are fixed and the area is to be maximized? ("most expansive"), or did you mean the cost is to be maximized for a given L ("most expensive") (as @janhardo seems to have assumed).

@C_R I think your red-circled green one should be yellow, not green - it is the outer integral integration variable.

Download RootOf.mw

@Jean-Michel 

Here is the excerpt from the file:

Do you agree? Because when I asked about this sequence starting with [1,2,7,...] you said no: "No Dharr I refer EXACTLY to the sequence given in the webpage I pasted here."

If I try these commands in Maple 2026, it works exactly as above:

Download test.mw

If I try the sequences in your original question, they both give FAIL as you found, which I believe is because Maple cannot solve them.

I enter xi (in math mode) in Scientific Word version 5.5. I select and copy and paste into a 2D input region in Maple 2026. lprint(%) gives "xi". Likewise, pasting into a 1D input region gives "xi". Please be more specific - are you using version 6? Which version of Maple?

Recent versions of Maple allow you to export the whole worksheet to latex. If you hide various parts, e.g., all Maple input then you can edit the output more easily to what you want. Not as good as a programmed solution as @acer suggests. See the help page

?worksheet,managing,exporttolatex

@Jean-Michel I'm sorry, I am totally confused and don't understand at all what you are asking. Hope someone else can help you.

@salim-barzani I think it is just too complicated for pdetest to finish. It works for some choices of the constants and functions that reduce the integrands to zero, but note that xi isn't real. Too many square roots of square roots in this case.

f-2s.mw

@Jean-Michel I think you are referring to the sequence on that page:

intseq := [1, 2, 7, 23, 85, 314, 1207, 4682, 18493, 73688, 296671, 1202849, 4910689, 20158436, 83169871, 344628527, 1433631973, 5984532728, 25060514887, 105240685511, 443102517025, 1870054761632, 7909539602647, 33521289826778, 142330494633985, 605375433105734, 2578988979186127, 11003364185437517];

That one can be solved - did you have a problem with that one? But that doesn't mean the other two sequences you chose can be solved.

@salim-barzani Note the comment about the magic of dsubs. Toward the end you had not substituted for P(y,t), a[1](y,t) etc. Now it works.

F7.mw