well ... hm ...

:-)

convert(v, exp); simplify(%); abs(%);

gives 1/2*2^(4/5)

The easy way would have been to do it during installation of Maple, one of the final steps ask whether it should open those files as default application.

I guess you are on Windows (because you say "PC").

After selecting one *.mw file through the context menu (=right mouse key) you can say "always open with" and can select the application through a dialog (you should however know where your maple is installed, for example "C:\Program Files\Maple2021\bin.X86_64_WINDOWS\maplew.exe".

Edit: Likewise you can use Windows' System Control to define which (standard) programs handle specific file extensions. That will depend on your Win version - and since I have a non-concurrent German version you better google for that way yourself (works for any pairing program & file extension)

1/12 + arbitrary constant is still an arbitrary constant

Your command says "cut at +-5 for the y-axis"

Try: plot((x^3 - 4*x^2 - 9*x + 36)/(x^3 - 9*x),  x = -3 .. 3);

It seems to dislike floating point numbers.

L:= convert(x2[1], rational);
numboccur(L, 0);

It is non-negative, but not strictly positive. You may look at

minimize(exp(x)+exp(y)+exp(z)+2*exp(-x-y-z), location);

I am rusty on this - but error 53 refers to run time libraries, so it is *.DLL and not *.xla

PS: you do not really want to post 2 very different questions in just 1 thread.

This is more a question of Numerical Analysis, you may start at https://en.wikipedia.org/wiki/Root-finding_algorithms#Roots_of_polynomials (which also mentiones the method suggested by Corless)

Using vv's suggestion to sum up over smaller intervals I get
0.005295 - 0.0009968*I for n=0 and 0.7493 - 0.4808*I for n=1
for epsilon = 1e-4.

My machines needs about 1.5 h for each case.

Find attached a solution using the NAG routines which gives
it in about 20 seconds for each case, giving the same figures.

MP_232754_NAG.mw

Likewise you write down the recursion function in Cents and finally express it in USD

B:=proc(m::nonnegint) # compute in Cents
round( B(m-1)*(1 + 0.0775) + 400000 );
end proc;
B(0):=400000: # initial

B(30)/100.0; # Cents as USD
                           470415.2400

Writing as iterated integral and handling s first I get
-0.331842471004086e-3 and -.663684942008173e-1

Edit: I have not treated the imaginary part correctly:

-0.331842471004085e-3 -0.331842471004085e-3*I and

-0.0663684942008172 - 0.0663684942008172*I

MP_232562_corrected.mw

MP_232562.mw

Look at plot([0*h[2](x), h[1](x)], x = 0 .. 6, y = -.1 .. .1)

PS: to find possible rounding errors do not use interface(displayprecision = 5), only if you are free of bugs

For Windows you may use its Indexer.

(p+1)*(p-1) = p^2 - 1 is zero modulo 3 by "Little Fermat" (except p=3). Hence one factor divides by 3 and being even (3<=p) it divides by 6.