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Stock-Based Compensation (Stock-Based Compensation Expense) (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]      
Stock-based compensation before income taxes $ 13,159 $ 13,286 $ 8,578
Income tax benefit (2,783) (2,840) (1,819)
Stock-based compensation after income taxes 10,376 10,446 6,759
Cost of Sales      
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]      
Stock-based compensation before income taxes 698 628 466
Sales and Marketing      
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]      
Stock-based compensation before income taxes 4,617 4,107 2,503
Research and Development      
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]      
Stock-based compensation before income taxes 1,931 1,777 1,236
General and Administrative      
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]      
Stock-based compensation before income taxes $ 5,913 $ 6,774 $ 4,373