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Formula to get the start date and end date of next week based on current date in apex.

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I don't think there is direct way. But you can do this.

date myDate = date.today();
date weekStart = myDate.toStartofWeek();
system.debug(weekStart.addDays(7) );

It will return the start of the week for the Date that called the method, depending on the context user's locale. example, the start of a week is Sunday in the United States locale, and Monday in European locales.

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