@Markiyan Hirnyk 

Yes, like you did these days for a similar question (=just feed original task, but with care),
though it needs much time at Digits=15 (lost patients for it).

Again I wanted know how to get rid of epsilon = smaller than preicsion ...

I would prefer to capture and move it with the mouse in the standard interface

For me it now is a question of (numerical) coding in C (using MS VC?). Best would be to get a book or lecture notes and to look into examples given by Microsoft. It will be time consuming to learn the stuff.

We can look into that. But please provide

a) code for copy+past (all your multiplication signs are missing, I do not want to fill them up)
b) info about your variables, parameters and return (what types: integer, floats and how you input them). Especially: what is alpha, beta?
c) from where you are going to use the DLL (calling convention)

To answer 1) you need an answer for 2) and c).
And you have to say what "dll function" should mean - to be used by what?

Actually for that I would use Compiler:-Compile and for a DLL this is covered by Maple's examples.

I have the impression you almost never coded an executable ... note that a DLL is just a specific EXE. I am not sure whether this is a Maple problem or more a question to be posted at a coding forum / learner's corner.

See also acer's remarks, posted before your reply ...

Anyway: you have to answer the questions first before continuing.

And please use the forum's Search Function, there are working examples at this board.

For that I use subs( int = Int, expression ) in case.

I do not know why the poster wants this. But having Int1 + Int2 and only one of it evaluates then what to do / to expect.

And I am not sure whether one should signal 'success' (silently? which one?) for any command. It would make coding difficult. Moreover results are often to be understood 'generically', they do not care for specific parameters.

May be the best would be a sketch what is intended

After all the replies you may say 1) what you expected as a numerical answer (from your theory, something like 7/15000) and 2) why you feed only 6 decimals (and not exact values, like 18.1818 = 200/11 or -exp(1)+2*exp(1/2) at other places) ?

Writing exp(h(eta)) / eta for the integrand one only needs to increase precision for h (by some Digits in a procedure), then it works. I could imagine that a reason might be: absulte errors for h give relative errors for the integrand (through exp, just like one should not compute powers through exp & ln for numerical needs)

PS: yes, I always initialize Digits=15 to have "hardware precision"

Thank you for pointing out that (and yes, your way is natural). I am not aware of an easy way over the Complex to re-write "abs" to get an algebraic task (either split C = R x R or use "Winding number" -> non-algebraic, at least formally)

I prefer that. And eval(%, abs= 't -> sqrt(t^2)' ) is a recipe over the Reals.

Under Tools-Options-Display 1st tab down the list one can see
a selection for Input Display. I have Maple Notation selected.

For output I have 2-D Math Notation. This way Maple 12 starts
up looking quite close to the Classic Interface, and it starts
with a (red) 'command line prompt', if setting the default by:

Change Tools > Options > Interface > Default format to 'Worksheet'.
(delivered default is Document here).

 If I hit the "insert button" in the menu bar, then I get what I desire.

@acer do you use some XML editor (and which one [ in case of] - though I am on Windows) ?

@Carl Love 

I think that - Pi^(3/2)*n should be + Pi^(3/2)*n and evaluating in integers has to be understood as limits.

Then the result seems to be correct

Edited: I withdraw, the correction is not so easy (looking at x= Pi/4 as an example, n ~ 2)

@Alejandro Jakubi 

I agree

"Latex ?" Better as plain text. Though better readable it would enforce readers to re-type instead of copy+paste.

It is not clear for me: What is your original function? A function of t only or a function of x and t?

You can try something like the following

f := (x, t) -> 1/(3*x - t - 2);

f(.1547196278, t);    # function to be 'approximated'
taylor(%, t=0, 5);    # this is a series
convert(%, polynom);  # now it is a polynom
plot(%);