Simplify the example script and rename examples #600

Job	Run time
Run linting/pre-commit checks	47s
Run linting/pre-commit checks	47s
Run linting/pre-commit checks	47s
check_docs	1m 1s
check_docs	1m 1s
check_docs	1m 1s
unit_tests (ubuntu-latest, 3.10)	6m 6s
unit_tests (ubuntu-latest, 3.10)	6m 6s
unit_tests (ubuntu-latest, 3.10)	6m 6s
unit_tests (macos-latest, 3.10)	4m 26s
unit_tests (macos-latest, 3.10)	4m 26s
unit_tests (macos-latest, 3.10)	4m 26s
local_integration_tests (3.10)	5m 54s
local_integration_tests (3.10)	5m 46s
local_integration_tests (3.10)	5m 50s
launch-slurm-actions-runner	0s
launch-slurm-actions-runner	0s
launch-slurm-actions-runner	1s
Run integration tests on the ${{ matrix.cluster }} cluster in job ${{ needs.launch-slurm-actions-runner.outputs.job_id }}	0s
Run integration tests on the ${{ matrix.cluster }} cluster in job ${{ needs.launch-slurm-actions-runner.outputs.job_id }}	0s
Run integration tests on the ${{ matrix.cluster }} cluster in job ${{ needs.launch-slurm-actions-runner.outputs.job_id }}	1s
Upload coverage reports to Codecov	0s
Upload coverage reports to Codecov	0s
Upload coverage reports to Codecov	1s
	54m 33s

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