As a rocket scientist you would definitely be doing lots of physics and math. Even if computers were doing the calculations, you might have to program them: not everything is solved with "off-the-shelf" software; and what do you think you are being paid for? However, there is nearly zero chance that you are going to be a rocket scientist. You walk around JPL or KSC, nearly every white-board is full of math symbols.
On a positive note, if you don't like calculations, you might consider engineering SALES, which can be very lucrative but involves only a little bit of figuring out problems -- in support of the customer. It's easiest to get into it if you have an engineering degree, but your day-to-day use of the academic material is limited.
Don't worry about that. Rocket Scientists study Physics or Aerospace engineering as a major and typically get their Masters and Ph.D's in Physics. Systems Engineers also commonly work for NASA and other satellite companies. They calculate the trajectory using nonlinear differential equations.
Heavy Math and Physics is typically used in Research and Development. R&D jobs typically require many years of experience and a Masters degree or better.
Most mechanical engineers work in manufacturing and construction, where more basic math and statistics/probabilities is used. In construction field working on plumbing and HVAC, you will have to know and use integration, fluid mechanics, fluid dynamics, and thermodynamics. You need to know those subjects to properly size motors and fans and pumps for the application so that the proper amount of hot/cold air and water get to all parts of the building.
The odds of you getting the job you describe is pretty slim. What you should do is get your degree and find a job that fits your interests and abilities regardless of the industry.
Mechanical engineering is very versatile so you can find a job just about any where if you have he grades.
More specifically If I want to be a Rocket scientist (design and test rockets for NASA or other space program). I'm afraid that if I finish my major in Mechanical engineering, and become a rocket scientist, they will make me do math and physics problems like I'm doing in right now in College. I just can't stand doing problems like this... I mean, I can do it, but it doesn't interest me at all, and I struggle a lot trying just to pass my classes. I don't want to continue towards this major just to find out I go to work and have to do the same tedious boring physics and math problems in order to calculate rocket trajectory, fuel efficiency, drag/friction, all that crappy stuff. Will there just be computers to do all those calculations for me? I don't know, please help me. I wanna enjoy my future Job, but I don't really know what to expect, I imagine sitting there at a computer doing all these ridiculous mathematical problems, and being bored and hating my Job, wishing I had done something easier because I'm not any sort of Albert Einstein. Non of this comes easily to me. I'm not a Genius.
