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Goodwill (Schedule of Goodwill by Segment) (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Goodwill [Roll Forward]    
Goodwill, net, beginning balance $ 861.7 $ 823.0
Currency translation and other 43.4 38.7
Goodwill, net, ending balance 905.1 861.7
Americas    
Goodwill [Roll Forward]    
Goodwill, net, beginning balance 146.6 143.2
Currency translation and other (0.3) 3.4
Goodwill, net, ending balance 146.3 146.6
Asia    
Goodwill [Roll Forward]    
Goodwill, net, beginning balance 171.9 172.7
Currency translation and other 2.8 (0.8)
Goodwill, net, ending balance 174.7 171.9
Europe    
Goodwill [Roll Forward]    
Goodwill, net, beginning balance 493.5 457.5
Currency translation and other 40.8 36.0
Goodwill, net, ending balance 534.3 493.5
Middle East and India    
Goodwill [Roll Forward]    
Goodwill, net, beginning balance 15.8 15.8
Currency translation and other 0.0 0.0
Goodwill, net, ending balance 15.8 15.8
Corporate and other    
Goodwill [Roll Forward]    
Goodwill, net, beginning balance 33.9 33.8
Currency translation and other 0.1 0.1
Goodwill, net, ending balance $ 34.0 $ 33.9