Dr:=proc(P::depends(list(And(ratpoly(integer,Variables),Not(integer)))),Variables::list(symbol),DEvar::symbol,DEsuffix::string)

PS. Note that ratpoly means rational function (such as (x+1)/(x*y+2)), not polynomial.

It is enough to set

_EnvFormal:=true;

Note that without this, even sum(p^k, k=0..infinity) is not computed. Of course one may use assume on parameters (in order to have convergence) but there are too many of them and I understand that your series are formal.

convert(a, cot);

I'd recommend to start with these much simpler integrals and see what happens:

int(sqrt(x^4+1),x);
int(sqrt(x^4+1+x),x);
int(sqrt(x^4+1+sqrt(x^2+1)),x);

restart;
with(LinearAlgebra):
t:=time():
n:=1000:
A:=RandomMatrix(n,n,generator=rand(-10.0..10.0),shape=symmetric,datatype=float[8]):
V,Q:=Eigenvectors(A):
MV:=DiagonalMatrix(sqrt~(Vector(V,datatype=complex))):
B:=Q.MV.Q^*:
`||A-B^2||`=Norm(A-B^2);
'time'=time()-t;

                                           
             ||A-B^2|| = 4.49369731341387095 * 10^(-11)  
                         time = 26.021

The integral `f*g` is expressed with the Dirac "function" and some problems appear.
Just convert f to Heaviside and it will work.
You may insert after your f:=...

f:=unapply( convert(f(x),Heaviside), x );

(Note that `f*g`(x) will be much simpler!)

Now OK :

TestCylinderInscritSphere-ok.mw

B:=copy(A);
Or,
B:=Matrix(A);

It is easy to see that this matrix was specially cooked to have no sqrt.

Its Jordan form is:

JordanForm(A);

but the first 2x2 block  [[0,1], [0,0]] does not have a square root, so A neither.

Edit.  Unfortunately I made a stupid (but hard to detect) mistake. The fact that a Jordan block does not have a sqrt does not imply that that the  whole Jordan form does not have sqrt; only the converse is true.

In this case, sqrt(A) exists (not unique of course) and can be computed. It is:

B:=Matrix(9, 9, [[2203/369+(41/135)*sqrt(5), 8665/1476+(14/45)*sqrt(5), 1145/246+(43/135)*sqrt(5), -1687/492+(44/135)*sqrt(5), 28/41+(1/3)*sqrt(5), -3979/1476+(46/135)*sqrt(5), -1315/738+(47/135)*sqrt(5), 125/492+(16/45)*sqrt(5), -3515/369+(49/135)*sqrt(5)], [-11015/1476+(41/135)*sqrt(5), -102365/5904+(14/45)*sqrt(5), 917/984+(43/135)*sqrt(5), 7451/1968+(44/135)*sqrt(5), -99/164+(1/3)*sqrt(5), 61223/5904+(46/135)*sqrt(5), -14089/2952+(47/135)*sqrt(5), 6263/1968+(16/45)*sqrt(5), 17575/1476+(49/135)*sqrt(5)], [4753/1476+(41/135)*sqrt(5), 102187/5904+(14/45)*sqrt(5), -5875/984+(43/135)*sqrt(5), -5149/1968+(44/135)*sqrt(5), -11/164+(1/3)*sqrt(5), -70897/5904+(46/135)*sqrt(5), 28319/2952+(47/135)*sqrt(5), -5281/1968+(16/45)*sqrt(5), -10001/1476+(49/135)*sqrt(5)], [-9539/1476+(41/135)*sqrt(5), -97937/5904+(14/45)*sqrt(5), 1409/984+(43/135)*sqrt(5), 7943/1968+(44/135)*sqrt(5), -99/164+(1/3)*sqrt(5), 59747/5904+(46/135)*sqrt(5), -15565/2952+(47/135)*sqrt(5), 4787/1968+(16/45)*sqrt(5), 16099/1476+(49/135)*sqrt(5)], [7705/1476+(41/135)*sqrt(5), 111043/5904+(14/45)*sqrt(5), -4891/984+(43/135)*sqrt(5), -4165/1968+(44/135)*sqrt(5), -11/164+(1/3)*sqrt(5), -73849/5904+(46/135)*sqrt(5), 25367/2952+(47/135)*sqrt(5), -8233/1968+(16/45)*sqrt(5), -12953/1476+(49/135)*sqrt(5)], [-5111/1476+(41/135)*sqrt(5), -72845/5904+(14/45)*sqrt(5), 1901/984+(43/135)*sqrt(5), 5483/1968+(44/135)*sqrt(5), 65/164+(1/3)*sqrt(5), 55319/5904+(46/135)*sqrt(5), -19993/2952+(47/135)*sqrt(5), 359/1968+(16/45)*sqrt(5), 11671/1476+(49/135)*sqrt(5)], [10657/1476+(41/135)*sqrt(5), 113995/5904+(14/45)*sqrt(5), -2923/984+(43/135)*sqrt(5), -7117/1968+(44/135)*sqrt(5), 153/164+(1/3)*sqrt(5), -64993/5904+(46/135)*sqrt(5), 16511/2952+(47/135)*sqrt(5), -9217/1968+(16/45)*sqrt(5), -15905/1476+(49/135)*sqrt(5)], [-11015/1476+(41/135)*sqrt(5), -137789/5904+(14/45)*sqrt(5), 4853/984+(43/135)*sqrt(5), 7451/1968+(44/135)*sqrt(5), -99/164+(1/3)*sqrt(5), 84839/5904+(46/135)*sqrt(5), -25897/2952+(47/135)*sqrt(5), 10199/1968+(16/45)*sqrt(5), 17575/1476+(49/135)*sqrt(5)], [4753/1476+(41/135)*sqrt(5), 49051/5904+(14/45)*sqrt(5), 29/984+(43/135)*sqrt(5), -5149/1968+(44/135)*sqrt(5), -11/164+(1/3)*sqrt(5), -35473/5904+(46/135)*sqrt(5), 10607/2952+(47/135)*sqrt(5), 623/1968+(16/45)*sqrt(5), -10001/1476+(49/135)*sqrt(5)]]);

# Proof:
Norm(A - B^2);
        0

delta is supposed to be in 0 .. 1

Then max(min(...)) = 1 - delta.

==> lim = 1 - delta

[You must use maths, not Maple for this].

Ok, I understand, when you write minimize, you mean maximize   :-)

In this case, maximize(abs(x^(2^(-t))-1),x=1-delta .. 1+delta);
equals (1-delta)^(2^(-t))  for t>0   [ hint:  u |--> (1+u)^alpha  is concave in (-1,1)  for 0 < alpha < 1 ]
Hence the limit (t--> oo) is:
limit((1-delta)^(2^(-t)), t=infinity);
                               1

You mean

g := (t,delta) -> minimize(abs(x^(2^(-t))-1),x=1-delta .. 1+delta);

But anyway g(t,delta) = 0, so the limit is 0 too.

http://www.bartleby.com/305/1009.html

It seems that all the plottools commands accept only Cartesian coordinates.
But, it is possible to use changecoords after that.

with(plots):with(plottools):
p1:=display(line([1,Pi/4],[2,Pi/2])):
p2:=changecoords(p1,polar):
display(p1,p2);

It is possible but not a very good idea.

You must rename your Rr procedure e.g. to RrProc because a table and a procedure cannot have the same name.

For example:
RrProc := proc(x,y)  x + y end proc:

`index/xxx` := proc(L) RrProc(op(L)) end proc: 
Rr := table(xxx):

Rr[6,7];
    13