There are probably a few ways to do this but I would not use Data Factory, unless you need to orchestrate this activity as part of a wider pipeline. As you have some compute handy via Azure SQL Database, I would make best use of that unless you have a specific reason not to do so. T-SQL has dynamic SQL and the EXEC
command to help. Use a cursor to run through the distinct list of formulas and execute it dynamically. A simplified example:
DROP TABLE IF EXISTS dbo.formulas;
CREATE TABLE dbo.formulas (
Id INT PRIMARY KEY,
formula VARCHAR(100) NOT NULL,
a INT NOT NULL,
b INT NOT NULL,
c INT NOT NULL,
d INT NOT NULL,
e INT NOT NULL,
--...
result INT
);
-- Set up test data
INSERT INTO dbo.formulas ( Id, formula, a, b, c, d, e )
VALUES
( 1, '(a+b)/d', 1, 20, 2, 3, 1 ),
( 2, '(c+b)*(a+e)', 0, 1, 2, 3, 4 ),
( 3, 'a*(d+e+c)', 7, 10, 6, 2, 1 )
SET NOCOUNT ON
-- Create local fast_forward ( forward-only, read-only ) cursor
-- Get the distinct formulas for the table
DECLARE formulaCursor CURSOR FAST_FORWARD LOCAL FOR
SELECT DISTINCT formula
FROM dbo.formulas
-- Cursor variables
DECLARE @sql NVARCHAR(MAX)
DECLARE @formula NVARCHAR(100)
OPEN formulaCursor
FETCH NEXT FROM formulaCursor INTO @formula
WHILE @@fetch_status = 0
BEGIN
SET @sql = 'UPDATE dbo.formulas
SET result = ' + @formula + '
--OUTPUT inserted.id -- optionally output updated ids
WHERE formula = ''' + @formula + ''';'
PRINT @sql
-- Update each result field for the current formula
EXEC(@sql)
FETCH NEXT FROM formulaCursor INTO @formula
END
CLOSE formulaCursor
DEALLOCATE formulaCursor
GO
SET NOCOUNT OFF
GO
-- Check the results
SELECT *
FROM dbo.formulas;
Cursors have a bad reputation for performance but i) here I'm using the distinct list of formulas and ii) sometimes it's the only way. I can't think of a nice set-based way of doing this - happy to be corrected. CLR is not available to you. If performance is a major issue for you you may need to think about alternatives; there's an interesting discussion on a similar problem here.
My results:

If your database was an Azure Synapse Analytics dedicated SQL pool then you could look at Azure Synapse Notebooks to achieve the same outcome.