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Stock-Based Compensation (Stock-Based Compensation Expense) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |
Stock-based compensation before income taxes | $ 13,286 | $ 8,578 | $ 8,135
Income tax benefit | (2,840) | (1,819) | (1,755)
Stock-based compensation after income taxes | 10,446 | 6,759 | 6,380
Cost of Sales |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |
Stock-based compensation before income taxes | 628 | 466 | 371
Sales and Marketing |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |
Stock-based compensation before income taxes | 4,107 | 2,503 | 2,069
Research and Development |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |
Stock-based compensation before income taxes | 1,777 | 1,236 | 1,032
General and Administrative |  |  |
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items] |  |  |
Stock-based compensation before income taxes | $ 6,774 | $ 4,373 | $ 4,663

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