Starting a job as an ME, I can say that you will probably spend some time learning basic dimensioning and tolerancing (which is not very well at all in college). You'll probably start with a solid model in some CAD software, make a drawing (Which is very easy nowadays), and dimension it. Your manager or supervisor will look it over, mark it up with a red pen, and you'll go over it again, correcting your mistakes. Eventually (this will happen quicker if your company actually manufactures it's own parts) you'll get the hang of it and your drawings will just be looked over by someone else. That, and you can get other new guys to do your drawings for you.
After that, you'll probably be fed some really simple parts to design. It probably won't take a whole lot of calculus, and you'll be relying on things like the machinists handbook and other standards (depending on your industry, some aerospace companies simply don't have standards to follow other than the companies, and those can change), but you will crunch the numbers and make the drawings.
You'll eventually take on bigger projects, teach some new guys the ropes, and begin to branch out even more.
If you don't find yourself making drawings and feeling satisfaction when you can see with your own eyes a piece that at one time only existed on paper and in your mind, I'd question my desire to become a mechanical engineer.
Now, I'm sure other ME's had a different experience, but I can't really comment on that.