It's unlikely that the parts of the questions that say: "Define <something> as" or "Define <something> to be" are asking you to do anything. I know it sounds like they're telling you to do something, but what those phrases really mean is that they have created a name for something and are telling you what that name means.
For example, if I said "Define the function f(x) to equal 1 when x > 0 and 0 when x <=0", then there's nothing for you to do. I'm basically telling you how to interpret expressions such as f(3). When you see f(3), I've just told you that f(x) = 1 when x > 0, therefore f(3) = 1.
If I said define a sequence a(n) so that a(0) = 1 and a(n+1)=a(n)+3, I've just told you how to interpret things like a(1), a(2), a(3). So I'm not telling you to actually do anything, I'm just giving you information so that you can understand the next things that I write.
We don't really do this in English because we don't really need to be constantly coming up with new names and symbols for things. But if I said to you that from now on when I say the word "ploof", I mean a "fluffy dog", then that would be the same as the mathematic directive: "Define 'ploof' to mean 'fluffy dog'".
Note: I'm just guessing here. I could very well be that a question is asking you to come up with your own definitions. I'd have to see the entire question and surrouding context to be sure.