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If it is any encouragement, most career in mechanical engineering are not math heavy. Going through the courses and understanding the math behind different concepts is crucial to the degree and applies to the work place, but more calculations or simulations are done with software, charts, material lists, and basic equations.
The reason it's important it for the deeper level of understanding. As an engineer, you need to identify when something is wrong or off about a result from those programs or equations. The base of knowledge allows you to quickly make forward moving decisions and identify concern areas. It's very useful and not something to be taken lightly.
Careers are, however, open book, open notes, open software, and (sometimes) open source. So math plays a part, but it's not as pronounced as in school.
Engineering is applied Math, Physics and Chemistry. Physics and Chemistry are both mostly based on Math. The vast majority of the sciences rely a huge amount of math today, far more so than in the past.
Get really good at Statistics - it is a very useful tool in all Sciences and Engineering.