In the statement:

F:=(a,b,c,d)->a*b*c*P(d);

the second argument, the list, is missing.

plot(surd(x,3),x=-10..10);

I do not beleive that Maple is (currently) very useful for Computational fluid dynamics.

To paste a picture, just use the "File Manager" (green upwards arrow icon) in the editor menu.

See e.g. ?plot,options :

font=l
This option defines the font for text objects in the plot where the value l is a list [family, style, size]....

See e.g. this thread.

In Maple I would use a piecewise, like:

f:=piecewise(x=0,0,0<x,log(x)*x,0);

                        {    0             x = 0
                        {
                   f := { ln(x) x          0 < x
                        {
                        {    0           otherwise

eval(f,x=0);
                                  0

I do not know, though the Matlab equivalent.

It would be more productive for trying to workout your super complicated expression if you post your input in text form or upload your worksheet.

What I know is that uploaded files cannot be deleted, but you can set them to private.

 For instance:

f:=(k1*A)/(k2*dA + CM*k3*k4):
MultiSeries:-series(f,e) assuming 0<m,m<1/7;


             m           (1 + m)        m 2   2   2     (1 + 2 m)
  k1 e   c[1]  k3 k4 k1 e          (c[1] )  k3  k4  k1 e
  ---- - ----------------------- + ------------------------------
   k2                  2                         2   3
                c[1] k2                      c[1]  k2

                m 3   3   3     (1 + 3 m)
           (c[1] )  k3  k4  k1 e
         - ------------------------------
                         3   4
                     c[1]  k2

                m 4   4   4     (1 + 4 m)
           (c[1] )  k3  k4  k1 e
         + ------------------------------
                         4   5
                     c[1]  k2

                m 5   5   5     (1 + 5 m)
           (c[1] )  k3  k4  k1 e
         - ------------------------------
                         5   6
                     c[1]  k2

And the same output from:

MultiSeries:-series(f,e) assuming 1/7<m;

May be combining curves like these two:

with(plots):
p1:=complexplot(eval((x+I*y)^4,[x=.5*(1+cos(t)),y=.5*(1+sin(t))]),
t=0..2*Pi):
p2:=complexplot(eval((x+I*y)^4,[x=.4*(1+cos(t)),y=.4*(1+sin(t))]),
t=0..2*Pi):
display(p1,p2,scaling=constrained);

One way is with subs:

subs((exp(a*x)+exp(b*x)+1)=exp(a*x)/p11,n);

                                       2
                              2     p11  b exp(b x)
                   a p11 - p11  a - ---------------
                                       exp(a x)

Note that a different name, has to be used instead of p1, as its value is exp(a*x)/(exp(a*x)+exp(b*x)+1).

What kind of expansion are you looking for? What do you know about m, e, etc?

If you mean less typing, it is not about the DETools package. You can do something like:

eq1:=diff(Q(t), t) = eta*(T(t)-theta)*s/l:
eq2:=diff(Q(t), t) = -c*m*(diff(T(t), t)):
eval(eq1,eq2):
dsolve({%,T(0) = `#msub(mi("T"),mn("0"))`});
                         /  eta s t\                                 
       T(t) = theta + exp|- -------| (#msub(mi("T"),mn("0")) - theta)
                         \   l c m /                                 

For that, there should not be bugs:

is(abs(argument(z))<Pi) assuming Re(z)>0;
                                false

Counterexample:

is(abs(argument(1))<Pi);
                                 true

is(Re(1)>0);
                                 true

And, presumably, Non(z<0) should be a property describing the condition that z is not a negative number:

is(Non(1<0));
                                 true

is(Non(I<0));
                                 true

is(Non(-1<0));
                                false

But this is wrong also:

is(abs(argument(z))<Pi) assuming Non(z<0);
                                false