I would be grateful if anyone would comment on the compatibility of Maple 18 and MacOS 10.10 (Yosemite).

Sorry if this is a well-known feature of Maple, but I haven't had much success searching for an answer.

Consider trying to separately solve each of the following two equations for x.

alpha * x + conjugate(alpha) * x = 1 

Maple 15 solves this equation to give x = 1/(alpha + conjugate(alpha)) , as expected.

alpha * x - conjugate(alpha) * x = 1

Maple 15 fails to solve this equation, returning nothing as if there is no solution.