[gaius]

Do you trust more your calculator when you have to perform simple operations like sums , multiplication or square root

I trust the calculator sure, but I try to always understand enough about the problem at hand to know when the numbers don't make sense - bad data, keying error, edge case, numeric overflow, wrong units, yadda yadda. Punching numbers in and blindly writing down what you get out is a recipe for disaster. When I did engineering it wasn't unusual for people to do the same calculations on an HP and a TI just to make sure - and bugs in calculators weren't unheard of.

base on computer simulations using well known and tested algorithms

SpaceX same as everyone else who actually does this, combines simulations and actual experiments. Noone flies anything built off simulations alone, and I can't see that happening for a looooong time. And even then, things still sometimes go wrong. Computers are not a magic silver bullet, they are just a tool like a spanner or a hammer.

[xHopen]

Didn’t NASA land a robot in mars without testing just base on simulations and law of physics , mainly because they couldn’t do in other way. Of course computers are a tool and not a silver bullet , but I trust more the computational power of a computer and the path taken base on algorithms in dangerous situations than a fragile human being