Several years ago, acer posted a topic on how to overcome the limitation of hardware precision plotting drivers in Maple:

https://www.mapleprimes.com/posts/100884-Precision-And-Plot-Drivers

Currently, I want to plot (1-x)^(10^9) in the range of 0..10^(-15) smoothly.

plot((1-x)^(10^9), x=0..10^(-15)) does not work. Is there an updated option to this in Maple since 2011? 

How can I get the equation G1 automatically shown in Latex as stated? Example:

G1 := V = Pi*(d/2)^2*h;

latex(G1);

# yields V=1/4\,\pi\,{d}^{2}h

rendered:

How can I make G1 inert so that Latex generator accepts it as input?

How can I typeset this in Maple? A ket with a 2 element column vector in it, but without the vector brakets. Like this:

| x over y >

Thanks

diff(sin(x)^2,x$n); # Maple fails

# then I tried:

combine(sin(x)^2);diff(%,x$n);

# this works, but Maple should drop the pochhammer term (derivation of a constant)

What is the reasoning behind the output?

I have reason to believe that the expression below is a real number: 

(1/6)*(-108+(12*I)*sqrt(1419))^(1/3)+10/(-108+(12*I)*sqrt(1419))^(1/3)+1;

A numerical approximation supports that. How can Maple help here to get a simplified expression?