I wouldn't use biomaRt, but try to use AWK instead. If you download the annotation gtf file from ensemble, you can try something like this with AWK:

awk '$3=="exon" {print $0}' Homo_sapiens.GRCh38.78.gtf | awk '{ count[$10]++ } END { for (word in count) print word, count[word]}' > numberOfExonsPerGene.txt

Or use R with a transcript database (you can make your own from any GTF using the makeTxDbFromGFF command from the GenomicFeatures library):

## setup transcriptDb
txdb <- TxDb.Mmusculus.UCSC.mm10.ensGene
## get exon locations for each gene
exons <- exonsBy(txdb,'gene')

## print number of exons for each gene - just look at the top 6 with 'head'
head(sapply(exons,length))
ENSMUSG00000000001 ENSMUSG00000000003 ENSMUSG00000000028 ENSMUSG00000000031 
                 9                  9                 24                 15 
ENSMUSG00000000037 ENSMUSG00000000049 
                41                 16

ucsc (not biomart)

$ mysql --user=genome --host=genome-mysql.soe.ucsc.edu -A -P 3306 -D hg38 -e 'select chrom,name,exonCount from wgEncodeGencodeBasicV28;'
+-------+-------------------+-----------+
| chrom | name              | exonCount |
+-------+-------------------+-----------+
| chr1  | ENST00000619216.1 |         1 |
| chr1  | ENST00000473358.1 |         3 |
| chr1  | ENST00000469289.1 |         2 |
| chr1  | ENST00000607096.1 |         1 |
| chr1  | ENST00000417324.1 |         3 |
| chr1  | ENST00000641515.2 |         3 |
| chr1  | ENST00000335137.4 |         1 |
| chr1  | ENST00000466430.5 |         4 |
| chr1  | ENST00000495576.1 |         2 |
| chr1  | ENST00000610542.1 |         4 |
| chr1  | ENST00000493797.1 |         2 |
| chr1  | ENST00000484859.1 |         2 |
| chr1  | ENST00000466557.6 |         8 |
| chr1  | ENST00000410691.1 |         1 |
| chr1  | ENST00000496488.1 |         2 |
| chr1  | ENST00000612080.1 |         1 |
| chr1  | ENST00000635159.1 |         2 |
| chr1  | ENST00000426406.3 |         1 |
(...)
+-------+-------------------+-----------+

I cannot see a a way either to directly get the number of exons in each transcript via biomart.

But you can choose Exon Stable ID as an attribute for an output. You can then use a simple awk script to count the exons per transcript. Let's assume you have choosen the attributes Gene stable ID, Transcript stable ID and Exon stable ID for the output. Make sure you tick the point "Unique results only" and download as a TSV.

$ awk -v FS="\t" -v OFS="\t" 'NR>1 {transcript[$2]++;} END { for(t in transcript) print t, transcript[t] }' mart_export.txt

This will create a list with the transcript name given in column 2 as the key, and count each line with this transcript number. At the end we iterate over the list and print each count. If the transcript id is in a different column in your output, change the $2 to whatever it is.

fin swimmer

Exon Number Finder v.1

A tool to find genes of user-specific exon number

https://github.com/CyPH3R-ASR/exonNum