@Rouben Rostamian  

Actually eq[2] is still undefined at (0,0,0). Maple does not see (without an extra simplify)  that the denominator is 0. 

@Carl Love 

The problem addressed by my answer was that strangely, fsolve is able to compute 4000 digits for z but not 5000.
Are you happy with this behavior?

It is strange that CubaCuhre works and other methods fail. After all, the function is well behaved so that any numerical integration should work. It seems that `evalf/MeijerG` is buggy.

@Carl Love 

Even when d=20 and we want 5000 digits for z (as above)?

@Mariusz Iwaniuk 

It seems that you have other integral in MMA.

@Markiyan Hirnyk 

Unfortunately you keep producing "anti-comments". It is a high school exercise to see that the equation 
arctan(x) = x/2 has 3 real roots and -tan(_Z) + 2 _Z = 0 has infinitely many real roots.

The important fact here is that RootOf uses a non-equivalent equation for the mentioned reason.

@Kitonum 

The name FrechetDistance for the procedure is misleading; this is actually a EuclideanDistance.
It would be interesting to compute the true FrechetDistance between the paths defined by P and Q.

@nm 

This is possible only if the expression has a single variabile. And even in this case the evaluation will produce _Z again.

Try:
expr:=RootOf(f(a, _Z, 1));

A better idea would be to define `print/RootOf`  but I think It's not worth it.

@acer 

At least for a single variable solve has the possibility to return a RootOf, so, if in doubt  it should never fail :-)

Example:
solve(floor(z)=1/2);
      RootOf(2*floor(_Z)-1)

@Adam Ledger 

If you are interested only in reals then use only the branches  0 and -1
(which contain the inverses of the restrictions of y = f(x) = x * exp(x)):

#  LambertW(-1,y),   y∈[-1/e,0)       ==>  x∈(-∞,-1]
#  LambertW(0,y),    y∈[-1/e,∞)       ==>  x∈[-1,∞)

plot(LambertW(-1,y), y=-exp(-1) .. - 0.01);
plot(LambertW(0,y),  y=-exp(-1) .. 100);

@nm 

At informal level blow-up is ok. But not beyond. Have you looked at the examples above?

Some examples (for both questions) of polynomials (non-trivial but not too complicated)  would be useful such that the (possible) responder has the possibility to test the answer.

@trace 

There are >1 solutions (actually an infinity if you don't need continuity).
If an exact solution is known, then use it of course.
If not, use fsolve and restrict if needed the range for p,v,w in order to find other solutions.

@nm 

"Blow-up" is not defined.  You probably mean  limsup_(x-->a) |f(x)| = oo. But singular does not mean this (see my first comment). For example:

singular(sin(1/x),x);  # it's bounded in R
                            {x = 0}
singular(1/(1+abs(exp(1/x))), x); # it's bounded even in C
          {x = 0}, {...}

@nm 

sqrt (the principal branch used by Maple) is continuous at 0.

For singularity, it depends on the definition. In complex analysis, 0 is a non-isolated singularity.