Your first round trip involves assigning a value to a variable, and retrieving that value when calling that variable. It's not a 'simple' variable, I know it's a matrix, but it's a variable anyway.
Your second round trip essentially defines a function, at least, it appears to do so. The definition:
sin(x):=0.5
States that, no matter what value x may have, sin(x) will always result in 0.5. The second part of this round trip could (better?) be:
And that shows that there's not one unique value of x for which sin(x)=0.5.
But in fact what you did is assign the value 0.5 to the variable named sin(x). This variable has no relation to a variable x whatsoever. It's similar to assigning:
In the meantime its well known and shown by quite some examples here in the forum that the new symbolic engine is much less capable than the old ones (muPad and even older Maple).
But as you are using Prime 6 you are lucky and can switch back to muPad at least (you can get rid of the second unnecessary "_n in Z" by adding the modifier "simplify").
or
Try the last one with the new engine for a funny experience.
