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Goodwill and Intangible Assets - Schedule of Intangible Assets and Goodwill (Details) - USD ($) $ in Millions | Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
--- | --- | --- | ---
Indefinite-lived intangible assets: |  |  |
Net goodwill | $ 80.7 | $ 93.7 | $ 98.6
Intangible Assets, Gross, (Including Goodwill) | 762.6 | 763.7 |
Accumulated amortization: |  |  |
Accumulated Amortization | 460.6 | 438.1 |
Intangible assets, net | 309.7 | 334.0 |
Business combination-related intangible assets, net |  |  |
Accumulated amortization: |  |  |
Net book value | 302.0 | 325.6 |
Trade names and trademarks |  |  |
Indefinite-lived intangible assets: |  |  |
Trade names and trademarks | 272.5 | 272.6 |
Capitalized internal-use software: |  |  |
Capitalized external-use software: |  |  |
Capitalized Computer Software, Gross | 40.1 | 38.1 |
Accumulated amortization | 32.4 | 29.7 |
Net book value | 7.7 | 8.4 |
Technology |  |  |
Finite-lived intangible assets: |  |  |
Technology | 118.6 | 119.6 |
Accumulated amortization: |  |  |
Accumulated Amortization | 97.9 | 95.3 |
Customer relationships and other |  |  |
Finite-lived intangible assets: |  |  |
Customer relationships and other | 371.5 | 371.5 |
Accumulated amortization: |  |  |
Accumulated Amortization | $ 362.7 | $ 342.8 |

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