@Kitonum 

They are so easy to compose ... E.g.

J := Int((2+ln(x))/(sqrt((ln(x)+1)*x)*sqrt(1-x-x*ln(x))), x);

ListTools:-Search is not faster; it actually calls member. Just type:

showstat(ListTools:-Search);

The error can be easily solved for Maple 2015 (probably in 2016 it's ok):

with(IntegrationTools):
f:=t^2*exp(-t)/ln(t):
J:=Int(f,t=0..infinity):
Change(J,t=exp(s)):
Split(%,[-eps,eps]):
J1,J2:=op(1,%),op(3,%):
J1a:=subs(t=s, Change(J1,s=-t,t)) assuming eps>0:
Jeps:=normal(combine(J1a+J2)):
J:=eval(Jeps,eps=0);

evalf(J);
    2.153547692

But the following theoretical problem appears.

If f is a function defined in an interval (a,b) having a singularity  s in (a,b),
h is a C^2 diffeomorphism from (a,b) to (c,d) and h is used as a change of variables
int(f, a..b) ---->  int(F, c..d)

then the following situations are possible:

1. f is integrable in the sense of Cauchy principal value but F is not.
2. F is integrable in the sense of Cauchy principal value but f is not.

@Axel Vogt 

Just consider

Int(a/x + 1, x=0..1)

for a-->0.

Edit. The changes of variables are in the intervals [0,1-a] (where the integral is not improper)
and [1+a, oo) where the integrability is obvious. (0<a<1).

I also vote up yours because it's general (it appears in Fihtengolts, you probably know this excellent textbook).

@Markiyan Hirnyk

@Markiyan Hirnyk 

1. I know those theorems (I teach measure theory BTW).

2. I asked Maple to compute the limit of the integral (not the integral of the limit). So, in principle, you should ask Maple to base its computations.
[I admit that Maple probably did not check the conditions].

3. It's not necessary to have uniform convergence. It's not difficult to use the Lebesgue dominated convergence for the integrand of J1+J2 (which, BTW, is not your expression).

@Declan 

f := (i,j) -> `if`(j=1, (i+4)^2, (i+4)^3):

@Declan 

The function (Maple procedure) f defines the (i,j) element of the matrix (i = row, j = column).

If j=1 then f(i,j) = i^2, otherwise (j=2 in our case), f(i,j) = i^3.

@Declan 

Why don't you use the clear and short preudocode algorithm at

https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test

Note also that you should not use FactorInteger (see the pseudocode above).
(BTW, FactorInteger is in the MmaTranslator; otherwise ifactors does the job).

Also note that your fea(x, e, n)  exists in Maple as  x &^ e mod n.

@JessyOw 

Have you tried the provided hint? Then the answer should be clear: you can't.

Yes, each letter is a polygon.
Unfortunately, the code is not mine and AFAIK such vector fonts are copyright protected (I do not know why, but that's it), so I cannot post them because I do not want to have problems.

@John Fredsted 

Groebner[Basis]( [x - a*b*y,y - a*b*x, a^2-1,b^2-1],plex(y,x,a,b)):
select(has,%,[x,y]);

@John Fredsted 

For polynomial systems you could use Groebner (which is what eliminate does, but you have more options).

Groebner[Basis](eqs,plex(x,a,y));

@Axel Vogt 

I asked the question because I was hoping that Maple 2016 will compute the integral directly. But both answers confirmed that this is not the case. They also contain the easy solution (integration by parts, any order) common for Maple 2015 and 2016.

@Christian Wolinski 

OP seems to be a beginner. Don't you think that a more useful procedure would have been

Cubic:=proc(p,x,a,b)
  local s,f,horizontals;
  f:=unapply(p,x);
  s:=solve(diff(p,x),x);
  horizontals:=map(f,[s])[];
  plot([p, horizontals], x=a..b, color=[red,blue,blue]);
end;

Cubic(1/3 *x^ 3 - 6/10 *x^ 2 - 187/100* x + 1, x, -3, 3);