ECAM has pointed the discussion in a relevant direction. In the real world we usually use computer prgrammes to solve the complicated problems and only the simple stuff is left to the human brain. As Ghengis says, you need to be very very good at algebraic manipulation but most of the rest is never used.
This may miss the point that in studying Mathematics we are learning the principles behind the design calculations. A quick read of Sir Stanley Hooker's autobiography "Not Much of an Engineer" will reveal the true relationship between higher mathematics and engineering. Sir Stanley was a PhD in Maths who designed jet engines using mental arithmetic. He also had the gift of being able to explain very complex engineering matters in simple easily understood ways. He could do this because he had an instinctive grasp of the mathematical principles.
We seldom consider the foundations of our houses, indeed we cannot even see them, but they are there nevertheless and the house wouldn't stand without them.
**********************************. .Through difficulties to the cinema