Checkered Tetrominoes

Puzzle description:
There are 10 different on-sided checkered terominoes which should be packed into a square or a rectangle with the correct checkerboard pattern.

The first goal of the puzzle is to select nine of the ten tetrominoes and pack them into a 6x6 square. The tray contains a space for the spare tetromino.
Note that a T-tetromino cannot remain as a spare tetromino, this can be shown with the usual parity argument. For eight different spare tetrominoes (except the T-tetromino) you have eight different tasks.

Additional goals are
* Fill a 5x8 rectangle with all tetrominoes.
* Fill a 4x10 rectangle with all tetrominoes.
* Difficult: Fill two 4x5 rectangles using all tetrominoes.

If you can read German: Mehr Informationen gibt es in https://welt-der-geduldspiele.blogspot.com/search?q=3D-Druck

Puzzle difficulty:
The puzzle may look easy, but some tasks are difficult. The number of solutions varies from task to task.

Printing instructions:
The main color (usually gray or