Should software accept ambiguous nonconforming mathematical formulas as input?

According to various international and national standards (e.g. ISO 80000 Quantities and units or DIN 1338 Writing and typesetting of formulae) as well as other guidelines (e.g. The International System of Units (SI)), ambiguous mathematical expression shall be avoided. In particular,

(…) a solidus (/) shall not be followed by a multiplication sign or a division sign on the same line unless parentheses are inserted to avoid any ambiguity.
_{ISO 80000-1:2009 Quantities and units – Part 1: General}

For example, the formula a/b*c is not permissible since it could mean a/(b*c) or (a/b)*c. The formula a/b/c is not permissible since it could mean (a/b)/c or a/(b/c).

However, typical spreadsheet programs (e.g. Microsoft Excel) and related software (e.g. for plotting curves) readily accept such ambiguous formulas. This behaviour can lead to unexpected results.

For example, this source of error can occur when a number in scientific notation such as 3.14E+03 is written as 3.14*10^3: The seemingly similar formulas 1/3.14E+03 and 1/3.14*10^3 have different results.

Another source of error in this context is the manual conversion of display-style formulas to suitable input expressions. For example, the equation

could be carelessly converted to the nonconforming formula k=A*exp(E/R*T), which would usually be accepted by the software and interpreted as k=A*exp((E/R)*T), although the intended formula is k=A*exp(E/(R*T)).

This leads me to the question whether such programs actually serve as a good model. Should a program quietly accept ambiguous mathematical formulas as input, or should it throw an error message?