doc: update spin lmp doc and example #10167

Job	Run time
Build source distribution	10s
determine-arm64-runner	1s
Build wheels for cp311-manylinux_x86_64	6m 11s
Build wheels for cp311-manylinux_x86_64	6m 2s
Build wheels for cp311-macosx_x86_64	6m 13s
Build wheels for cp311-macosx_arm64	2m 26s
Build wheels for cp311-win_amd64	5m 35s
Build wheels for cp310-manylinux_aarch64	6m 11s
build_pypi_index	1s
build_docker (12)	1s
build_docker (_cu11, 11)	1s
upload_pypi	0s
deploy_pypi_index	1s
Pass testing build wheels	4s
	32m 57s

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