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Intangible Assets (Acquired Intangible Assets) (Details) - USD ($)
$ in Millions
Sep. 30, 2023
Sep. 30, 2022
Goodwill and Intangible Assets Disclosure [Abstract]    
Intangible assets, gross $ 672.3 $ 636.2
Accumulated amortization and impairment (337.7) (288.7)
Intangible assets, net 334.6 347.5
Acquired Finite-Lived Intangible Assets [Line Items]    
Finite-lived intangible assets, gross 625.1 594.0
Accumulated amortization (327.6) (279.6)
Finite-lived intangible assets, net 297.5 314.4
Trade names and trademarks    
Acquired Indefinite-lived Intangible Assets [Line Items]    
Indefinite-lived intangible assets, gross 47.2 42.2
Accumulated impairment (10.1) (9.1)
Indefinite-lived intangible assets, net 37.1 33.1
Customer relationships    
Acquired Finite-Lived Intangible Assets [Line Items]    
Finite-lived intangible assets, gross 507.3 487.5
Accumulated amortization (262.2) (226.3)
Finite-lived intangible assets, net 245.1 261.2
Patents and technology    
Acquired Finite-Lived Intangible Assets [Line Items]    
Finite-lived intangible assets, gross 41.1 33.1
Accumulated amortization (26.7) (16.3)
Finite-lived intangible assets, net 14.4 16.8
Other    
Acquired Finite-Lived Intangible Assets [Line Items]    
Finite-lived intangible assets, gross 76.7 73.4
Accumulated amortization (38.7) (37.0)
Finite-lived intangible assets, net $ 38.0 $ 36.4