Learn English – What do we call these ‘squeezed’ papers

The first is often called a mister - a device, such as a bottle, with a nozzle for spraying a mist of water, esp. on houseplants.

The second is often called a CD cakebox, defined by Google as...

1: A storage container for a round layer cake, with a surrounding cover that protects and preserves the cake.
2: A similarly shaped package for blank, recordable compact discs, with a central spindle on which discs are stacked.

As implied by that second definition, if OP specifically wants to refer to the "pole" in the middle, it's always called the spindle.

Booklet can work and depending on what information is being conveyed it may be the best choice. If the pages expand on an subject the teacher is presenting, booklet is probably best.

Handout, as suggested, is also correct but handout is extremely generic. If I give you one sheet of paper in class, that is also a handout.

Pamphlet is a good word for stapled together sheets but that word also implies that the papers provide information on a single subject. If, for example, the handout is actually your class syllabus then pamphlet doesn't really work.

The simplest solution is to refer to stapled together pages more specifically. If it's the class syllabus call it that. If it's a brochure promoting condos in Hawaii call it a brochure.