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Place the pieces of fruit, sugar, and water in a small saucepan. Set the saucepan on the stove.  A few different fruit options worth considering include: blackberry, strawberry, raspberry, blueberry, mulberry, cherry, pineapple, apple, and mango. Finely chopped rhubarb stalks are another option. Unless you're using small berries, dice the fruit into 1/2 inch (1.25 cm) pieces before adding it to the saucepan. Set the stove to medium heat and gradually bring the contents of the saucepan to a simmer, stirring occasionally. Place the lid on the saucepan and cook the contents for 10 minutes, stirring occasionally, until the sugar completely dissolves and a moderately thick syrup forms. Note that the color of the syrup should be similar to the color of the fruit at this time. The fruit itself should be significantly softened. Pour the contents of the saucepan through a sieve. Collect the syrup and discard the solid chunks of fruit. To squeeze out as much flavor from the fruit as possible, lightly mash it with the back of a fork or mixing spoon before pouring the contents of the saucepan through the sieve. Allow the syrup to cool to room temperature before using it for an Italian or French soda.  For best results, let the syrup cool at room temperature on your kitchen counter. If you need to speed things up, cool it for 30 to 60 minutes in a refrigerator. Do not add warm syrup to the Italian soda since it will cause the ice to melt too quickly. Store any excess syrup in the refrigerator.
Combine the ingredients in a small saucepan. Heat to a simmer. Cover and cook for 10 minutes. Strain the syrup. Cool before use.