@digerdiga 

In the CPV sense the integral converges. The problem is more maths than Maple. When I'll have time I'll post a solution at the Application Center.
In the mean-time here is a table of values. Observe some kind discontinuities at t=0 and t=±2 where the ordinary Riemann integral does not exist. I am going to investigate the case of irrational t (but this seems to be a tough task and Maple cannot help at all).

F(-21/10) = -1.34045072401727*I
F(-20/10) = -.995421082418696*I
F(-19/10) = -.562990651564561*I
F(-18/10) = -.622200895257619*I
F(-17/10) = -.687638334639360*I
F(-16/10) = -.759957889597397*I
F(-15/10) = -.839883358545194*I
F(-14/10) = -.928214662439857*I
F(-13/10) = -1.02583585065994*I
F(-12/10) = -1.13372394886877*I
F(-11/10) = -1.25295873741565*I
F(-10/10) = -1.38473355814056*I
F(-9/10) = -1.53036725774037*I
F(-8/10) = -1.69131738722984*I
F(-7/10) = -1.86919478960212*I
F(-6/10) = -2.06577972168680*I
F(-5/10) = -2.28303967155866*I
F(-4/10) = -2.52314904981962*I
F(-3/10) = -2.78851095183085*I
F(-2/10) = -3.08178120869891*I
F(-1/10) = -3.40589496772606*I
F(0) = -1.95029670411682*I
F(1/10) = -.150852890432947*I
F(2/10) = -.166718227414152*I
F(3/10) = -.184252136451252*I
F(4/10) = -.203630102799237*I
F(5/10) = -.225046067658478*I
F(6/10) = -.248714369203441*I
F(7/10) = -.274871887751179*I
F(8/10) = -.303780416539164*I
F(9/10) = -.335729281839998*I
F(10/10) = -.371038238635994*I
F(11/10) = -.410060670834519*I
F(12/10) = -.453187128052909*I
F(13/10) = -.500849234370305*I
F(14/10) = -.553524008166522*I
F(15/10) = -.611738636282314*I
F(16/10) = -.676075750282477*I
F(17/10) = -.747179257628374*I
F(18/10) = -.825760786120238*I
F(19/10) = -.912606806107378*I
F(20/10) = -.522580426869140*I
F(21/10) = -0.404209101674264e-1*I

When I said that the integral converges I had in mind the case t = 1.
For t = 0 it obviously diverges; however it converges in the sense of Cauchy Principal Value.
As a standard Riemann integral I was able to prove the convergence only for a rational t = m/n and m = odd. For t=2 the integral diverges.

@Carl Love 
This was my first idea too. But the speed gain is < 50% and the memory used is high.

@acer 

Thank you for the info. I have never used Grid:-Seq. At least for this example it's faster than Threads:-Seq.

@Axel Vogt 

The integral converges by Abel-Dirichlet test.
(Non-absolute; it diverges as a Lebesgue integral).

OK, it seems that local in add is mandatory!

f:= proc(a,b) local j; add(evalf(j), j=a..b) end;

@Carl Love 

Finding m,e knowing m^e and e = small  is easy. In RSA the difficulty is to factor p*q where p,q are very large primes.
Maybe I did not understand correctly the question.

As I understand, you have to find m,e  knowing N = m^e.
That's not very complicated. Using ifactor(N, squfof)   it will be easy to guess/find them.
Try e.g. N:=
5283597479841597502249307485588838844324473186573614855471562459448464828552735855088707462629612291598041514584904540472660494110653291932470075292547145210822324745155897560267036743476680221427790422110515202011964431471384842095573958377510093885637085734820168772718612273735147472070258932628775898758897412226488939057837979980769415961378222304261197320528934891951607747393043656614642594700809003459632409006066267138249024446294095156593548315728936040653789120591837824475755907379232018649223902950942975775037420705139329445433146351673057179703495785985220713437280121677906674143134378403844456783699415097102039872927189701943998616449477694388377702044253596613030040326758555708583267301883314125107545253446831063342441728616341240949066395211515939602294216321926398675848886769810676117856035829363333298079191448903368142757335242512722676706735845656490815025862238130000276171518155874885468257512541410924692110161380057047725632895137485759966656826739299402437133339609007048080319742614535657702844659707293728211074016418040732570497677788259855095483525018056307607306278243462315486214465647363216751359562760677475255078172901823985688329458599220596044067226315768226821751699260397209688087591938373580424040307028260538131851994123858085534461046022284881587610082674005832606592209828845147906135954713649332888568291180195464612224361238254391785173060931665558390367225308286969618431118120976991981447101202958924337401723736512961037932697589586335779865946133100187875554605802539552426097002715212600249454709217394893695378126176694342996696751208835388019722156879855262771584638284999360304523228551093176774637915758542914188602048723477733930925536868256601511165330660464439486195411166058393929945245444434251599591492241478220969437007261767825127964591926196752782936064796117603667827244682010772179531705129073600636204263059314622817828202560482128186934449443409331011725081193850510470895634609488469170317013399523170035926302543347877450282268754145736859354780904868123578990812859018889776677551049226315751602790562810600914111735927913154944143705021038930617537747065116738052048909074156490455503896978413993243477083956694948752752672390069742003946479941632492376010095167332610543644372885072510976

If ifactor does not work and  e is not too large, try
is(N^(1/e), integer);  for e=2,3,...

@Carl Love 

nops(select(p-> nops(p)=3, combinat:-partition(n,n-2))):
is much slower than
nops(sort~(composition(n, 3)));
for n=80 say.

But when k >>3 the situation is reversed.

@mehdi jafari 

numbperm([1,1,5]);
    3

@Joe Riel 

Thank you. The idea of using a table with list indices is indeed very efficient.
P.S. It's not clear which part does not seem to be important:
(a) removing the duplicates, or
(b) avoiding to re-create the vectors.

@Carl Love 

A more important question is to find an efficient way for removing the duplicates from a set containing mutable elements.
For example,
S:={seq(LinearAlgebra:-RandomVector(2, generator=rand(0..2)),i=1..20)};
Here a solution is to convert the vectors to lists and then back.

@Carl Love 

Seems to be perfect now.

@Carl Love 

I get exactly:
real
real intersect RealRange(-infinity, 1)

evalb(real=RealRange(-infinity, infinity));
     true

@Carl Love 

Now for ex1 I get "real". For ex2: "real intersect (-oo,1) "  as before.
Note that RealRange(-infinity, infinity) is automatically simplified to "real".