Share-Based Compensation (Schedule of Share-Based Compensation Expense) (Details) - USD ($) $ in Thousands	12 Months Ended
Aug. 31, 2026	Aug. 31, 2025	Aug. 31, 2024
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	$ 5,826	$ 8,236	$ 6,496
Tax benefit	(882)	(1,699)	(1,527)
Share-based compensation expense, net of tax	4,944	6,537	4,969
Location, Statement of Income, Balance [Axis]: us-gaap:CostOfRevenue
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	180	169	183
Location, Statement of Income, Balance [Axis]: us-gaap:GeneralAndAdministrativeExpense
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	5,085	7,240	5,473
Location, Statement of Income, Balance [Axis]: us-gaap:OperatingExpenses
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	5,646	8,067	6,313
Location, Statement of Income, Balance [Axis]: us-gaap:ResearchAndDevelopmentExpense
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	159	214	190
Location, Statement of Income, Balance [Axis]: us-gaap:SellingExpense
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total share-based compensation expense	$ 402	$ 613	$ 650

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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+ Details