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Stock-based Compensation Plans (Schedule of Share-based Compensation. Option Activity (Details) - USD ($)
$ / shares in Units, $ in Millions
 12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Exercised, shares (246,577) (517,839) (110,989)  
Stock Options, Exercisable, Number 374,295      
2006 Plan        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Outstanding, shares 931,770 1,127,468 1,013,293  
Outstanding, Weighted average exercise price (per share) $ 15.89 $ 12.60 $ 12.10 $ 12.19
Outstanding, Weighted average remaining contractual term, years 7 years 9 months 18 days 7 years 10 months 24 days 7 years 9 months 18 days 7 years 8 months 12 days
Outstanding, Aggregate intrinsic value $ 8.8 $ 8.5 $ 1.0 $ 0.3
Granted, shares 228,615 457,356 573,279  
Granted, Weighted average exercise price (per share) $ 25.54 $ 13.22 $ 11.41  
Exercised, shares (246,577) (517,839) (131,989)  
Exercised, Weighted average exercise price (per share) $ 12.33 $ 12.05 $ 9.59  
Exercised, Aggregate intrinsic value $ 3.3 $ 5.0 $ 0.4  
Canceled, shares (5,604) (135,215) (327,115)  
Canceled, Weighted average exercise price (per share) $ 19.45 $ 12.69 $ 12.16  
Outstanding, shares 908,204 931,770 1,127,468 1,013,293
Stock Options, Exercisable, Number 374,295      
Exercisable, Weighted average exercise price (per share) $ 12.60      
Exercisable, Weighted average remaining contractual term, years 6 years 9 months 18 days      
Exercisable, Aggregate intrinsic value $ 4.8