Have you looked up the help for that command?

for that kind of postings you / one should earn a negative rating, it is more than lame

Just a remark and ignoring the problem with "timelimit":

If it does not finish within hours then for me it would be likely that concurrent Maple can not solve the integral as given. Probably I would accept that (especially: the result could be wrong) instead of hoping for "brute force". May be you could find a better input by analyzing the mathematical structure. Or restrictions for the parameter a. Or for the range of p.

Thank you for completing :-)

@delvin that are just those you uploaded

1.mw = Version 2023.2
2.mw = Version 2022.2

Note also that Psi might be understood as the Psi function of Maple

@andmail

That code looks by increments of 1e-4 until something is ok, needing ~ 9000 steps. Perhaps you better look for a zero finder in VBA, "bisection" is certainly available. Or use the goal seek in an Excel sheet

Setting X = x/C you can write it as 0 = x - C*sin(x), which is a special case of Kepler's equation,
https://en.wikipedia.org/wiki/Kepler%27s_equation

Now use suggestions from that Wiki article or search for VBA code.

From your pdf it is likely that it is Brent's minimizer. If you can not find it through your search engine then I can upload an old post of Devore from the usenet (= http://groups.google.com today). However in Maple you will not need that, I guess.

At least if I use MMA-online I get quick results. But they are not consistent:

https://www.wolframalpha.com/input?i=evalf%5B15%5D%28LerchPhi%281%2F10%2C+1%2C+1%2F2-100000000*I%29%29
~ 1.018518518518518×10^(-15) + 1.666666666666667×10^(-7) i
https://www.wolframalpha.com/input?i=evalf%5B45%5D%28LerchPhi%281%2F10%2C+1%2C+1%2F2-100000000*I%29%29
~ 3.055555555555555×10^(-15) + 5.000000000000000×10^(-7) i

Similar for the original task (see attached sheet)

MP_236256.mw

I changed the Title from "how to solve for lamda and r in this equtaions.?" to "how to solve cos * cosh = 1 ?"

@sursumCorda

For Optimization:-Minimize(F(x,y,z) Maple (*) returns "Error, (in Optimization:-NLPSolve) no improved point could be found", at least it should report the point and the value

Playing with 'minimize' gives some strange answers (or even none)

(*) Using Maple 2021.3, I do not have 2023

@toran about what you want to write, who will read it?

Download page: https://www.maplesoft.com/download/

Then enter your purchse code (= the one after "The following Purchase Codes activate this product")

@Carl Love Thank you, my fault (guess I believed the search function)