So I just stumbled upon the wikipedia page for squaring the circle and learned that it's impossible to do with only a straightedge and compass.
Is this possible if we are allowed to use any other simple tools, or do we need something to do arbitrary calculations for us(like a calculator)?
On
It suffices to have two marks on your straightedge, one at distance $1$ from one of the sides, and one at distance $\sqrt{\pi}$.
You can then use the intercept theorem to construct $r\sqrt{\pi}$, where $r$ is the radius of the original circle, and since a square with sides of length $r\sqrt{\pi}$ has area $r^2 \pi$, you have then squared the circle.
If you don't like the idea of marks on your straightedge, you could also use a right-angled triangle whose side lengths (of the two sides encompassing the right angle) have ratio $\sqrt{\pi}$. That, again, allows you to multiply arbitrary lengths with $\sqrt{\pi}$.
The questions becomes more interesting if you ask for tools to trisect an angle, instead. There are devices which allow you to do that, but they aren't quite a simple as the one above for squaring the circle.
I believe the extra tools we sometimes see discussed, as for trisecting arbitrary angles, are restricted to finding certain algebraic numbers, not transcendental, so no.
On the other hand, if we switch to the surface of a sphere, it is fairly easy to produce (some thought is needed ahead of time to do this by the rules) a circle around the North Pole and a "square" with the same area. A square will be bounded by four arcs of great circles, of the same length, with corner angles equal; these angles will be larger than $90^\circ.$
The limiting case of this is simply the equator itself, which is both a circle around the North Pole and a "square" with all four angles equal to $180^\circ$