Maple and Wolfram Alpha showing different answers for simple calculation

Question

I put this into Maple

$Y(a, y):= 2^a-2^a*y((1-y)^2)-\sqrt(1/2^a) $

$Y(0.5, 1/2); -0.1337896344$

and this into Wolfram Alpha

$2^{1/2}-2^{1/2}*(1/2)((1-(1/2))^2)-\sqrt(1/2^{1/2}))=0.37$

How is this possible??

Answer 1

As is pointed out in the comments, the problem with the Maple code is that the y(...) term is using y as a function application.

When you evaluate your code, you get y(...) = 0.5(...). In Maple, for the case that you have an expression such as 0.5(x), it represents the constant function 0.5 (the function that is 0.5 everywhere); the result of evaluating it is the number 0.5. This would account for the differing result.

The valid Maple code that you should input is:

Y := (a,y) -> 2^a - 2^a*y*((1-y)^2)-sqrt(1/2^a);
Y(0.5,0.5);

returns:

.3965404516

Also, note the slight difference in the function declaration in the code above.