You post so many almost identical questions.
Here, the answer of your question why simplify does not work on this example? - MaplePrimes
applies ad litteram (but for x>0 now).

You have syntax erors. Use:

s := Maximize(TRC(tau1, lambda), C3 union C5, tau1 = 0 .. 1, lambda = 0 .. 1, assume = nonnegative);

What polynomials are congruent to u(x) modulo  p(x).

Answer: the equivalent class   < rem(u(x), p(x), x) > 
i.e.  rem(u(x), p(x), x) + A(x)*p(x),  where A(x) is an arbitrary polynomial,

Your example: 

rem(x^2+x+1, x+1, x) + A(x)*(x+1);  # for A(x)=x ==>  x^2+x+1

                               1 + A(x)*(x + 1)

In the last loop:
-  Insert a space between from and 1
and
-  replace sum with add.

Li is in the sense of Cauchy principal value, so, you must use:

int(1/ln(x),x=0..X, CPV);
#                           Ei(ln(X))

convert(%, Li);
#                             Li(X)

Just use := for assignments, instead of =.
So, 

n1 := 423; x := 16;   etc

Use

map(eval~, M);

The integral is + infinity for any real A,B.
Just evaluate:

integral assuming B>0;
and
integral assuming B<0;

Or, compute asympt(integrand, p, 1);

  lim   (x ln(x)) =   lim   ln(x) / (1/x) =    lim   (1/x) / (-1/x^2) = 0
x -> 0+             x -> 0+                  x -> 0+     

Example

Download groeb1vv.mw

f := (x, y) -> piecewise([x, y] = [0, 0], 0, (x^3*y - x*y^3)/(y^2 + x^2)):
f(0,0);
#                               0

fx0:=limit((f(x,0)-f(0,0))/x, x=0);
#                            fx0 := 0

fy0:=limit((f(0,y)-f(0,0))/y, y=0);
#                            fy0 := 0

limit(( f(x,y)- fx0*x - fy0*y )/(x^2+y^2), [x=0,y=0]); 
#                            -1/4 .. 1/4

 ==> f has partial derivatives (both are zero) at (0,0)

 but it is not differentiable at (0,0).

restart;
phi := (p__1, p__2, q__1, q__2, xi) -> p__1*exp(q__1*xi) - p__2*exp(q__2*xi):
xi:=2:   # <----
for p__1 in [0,1,-1,I,-I] do
for p__2 in [0,1,-1,I,-I] do
for q__1 in [0,1,-1,I,-I] do
for q__2 in [0,1,-1,I,-I] do
  result1 := evalf(phi(p__1, p__2, q__1, q__2, xi));
  print('phi'(p__1, p__2, q__1, q__2, xi)=result1);
od od od od:

Don't use the dot (.) operator for usual multiplication; it is reserved for noncommutative multiplication  (usually dot product) . Use * instead.
For example,

simplify(v . ( 2/v + 1));
is not simplified if v is a name.

1. Use
showstat(DEtools:-odeadvisor);
or better:
showstat(DEtools[odeadvisor]);
because DEtools is a table-based package.

2.

stopat(DEtools[odeadvisor]);
 #                    [DEtools[odeadvisor]]
ode:=y(x)*(2*x^2*y(x)^3+3)+x*(x^2*y(x)^3-1)*diff(y(x),x)=0;
DEtools[odeadvisor](ode);

If possible, don't use floats in symbolic computation (here limit)

Compare:

limit(n*(1/3 - 1/(3+1/n)),n=infinity);
#                               1/9
limit(n*(1/3. - 1/(3+1/n)),n=infinity);
#                        -Float(infinity)

So, replace in W:  3.6  with 36/10  etc.