The second result is definitely wrong, but why is this? 

MmaTranslator:-FromMma("Subscript[x, 0] -> 2 (y - z) (y - z)");
                       

MmaTranslator:-FromMma("Subscript[x, 0] -> 2 (y - z)^2"); # should return: x[0] = 2*(y - z)^2
                      

The result is still wrong even if I type an explicit multiplication sign (for instance, "Subscript[x, 0] -> 2*(y - z)^2"). 

There exists a new (?) checkbox  in the Interface tab of the Options dialog: 

But I cannot find any find any explanation about it in the corresponding help page. What is the purpose of this feature? 

If I understand correctly, both of 

int(RETURN(is(y::positive)), y = 0 .. x) assuming 0 <= x, x < 1;
int(RETURN(coulditbe(y = 1)), y = 0 .. x) assuming 0 < x, x < 1;

should output . However, Maple simply returns  for the second one. 
Isn't this result incorrect? Or am I missing something?

OEIS A034828 and OEIS A000292 (which give the Wiener index for the cycle graph and the path graph respectively) mention that 

However, 

GraphTheory:-WienerIndex(GraphTheory:-CycleGraph(19));
 = 
                               38

GraphTheory:-WienerIndex(GraphTheory:-PathGraph(20));
 = 
                               38

So what happened here? 

Consider the following exact algebraic number : 
 

Download wrong_minpoly.mw 
I would like to find its minimal polynomial (without a priori knowledge). 

According to the documentation, 

Regretfully, it is easy to see that the minimal polynomial of  cannot be the returned . And when I invoke  directly, the result is still not correct (and this evaluation takes a rather long time). 
Another help page mentions that 

However, as type(mp, polynom(rational, _X)) gives , we know that cannot be the desired minimal polynomial of either. 
So, what is the proper way to compute the minimal polynomial of  in Maple? 

Code: 

use alpha=1-(1/2)/(1-(RootOf(16*_Z*(_Z*(2*_Z*(_Z*(8*_Z*(_Z*(_Z*(_Z*(32*_Z*(8*_Z-33)+1513)-812)-13)+267)-1469)-330)+811)+279)+345,index=2)-1/2)**2) in 
	expr:=(1+alpha)*sqrt(1-alpha**2)+(3+4*alpha)/12*sqrt(3-4*alpha**2)+2*(1+alpha)/3*sqrt(2*(1+alpha)*(1-2*alpha))+(1+2*alpha)/6*sqrt(2*((1-alpha)**2-3*alpha**2)) 
end:
CodeTools:-Usage(PolynomialTools:-MinimalPolynomial(expr));

Of note, the minimal polynomial of an algebraic number  is the unique irreducible monic polynomial of smallest degree  with rational coefficients such that  and whose leading coefficient is 1.